B
1) If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.
A) True
B) False
B
2) Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum
A) is equal to 2.0 m.
B) could be as small as 2.0 m or as large as 12 m.
C) is equal to 12 m.
D) is equal to 8.
C
3) Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?
A) 10 mm
B) 20 mm
C) 40 mm
D) 80 mm
B
4) The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.
A) True
B) False
Between 7.0 m and 17.0 m
5) A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?
B
6) If + = and their magnitudes are given by A + B = C, then the vectors and are oriented
A) perpendicular relative to one other.
B) parallel to each other (in the same direction).
C) antiparallel to each other (in opposite directions).
D) It is impossible
A
7) If - = 0, then the vectors and have equal magnitudes and are directed in the same direction.
A) True
B) False
B
8) If three vectors add to zero, they must all have equal magnitudes.
A) True
B) False
D
9) The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is
A) 90�
B) 180�
C) 60�
D) 0�
E) 270�
D
10) The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is
A) 0�
B) 90�
C) 270�
D) 180�
E) 360�
C
11) Vectors and obey the equation + = 0. These vectors satisfy which one of the following statements?
A) Vectors and are at right angles to each other.
B) Vectors and point in the same direction.
C) Vectors and have the same magnitudes.
D) The magnitude o
C
12) Consider two vectors and shown in the figure. The difference - is best illustrated by
A) choice (a)
B) choice (b)
C) choice (c)
D) choice (d)
B
13) Consider two vectors and shown in the figure. The difference - is best illustrated by
A) choice (a)
B) choice (b)
C) choice (c)
D) choice (d)
(a) B (b) A
14) Refer to the figure, which shows four vectors , , , and .
(a) Vector as expressed in terms of vectors and is given by
A) + .
B) - .
C) - .
(b) Vector as expressed in terms of vectors and is given by
A) + .
B) - .
C) - .
B
15) If a vector's components are all negative, then the magnitude of the vector is negative.
A) True
B) False
A
16) The magnitude of a vector can never be less than the magnitude of any of its components.
A) True
B) False
A
17) The magnitude of a vector an only zero if all of its components are zero.
A) True
B) False
B
18) If a vector has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0� to 90�
B) 90� to 180�
C) 180� to 270�
D) 270� to 360�
E) It cannot be determined without additional information.
C
19) If a vector has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0� to 90�
B) 90� to 180�
C) 180� to 270�
D) 270� to 360�
E) cannot be determined without additional information
D
20) If a vector has components Ax > 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0� to 90�
B) 90� to 180�
C) 180� to 270�
D) 270� to 360�
E) cannot be determined without additional information
D
21) The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements must be correct for these two vectors?
A) Vector is parallel to vector .
B) Vector is antipar
D
22) Vector is along the +x-axis and vector is along the +y-axis. Which one of the following statements is correct with respect to these vectors?
A) The x component of vector is equal to the x component of vector .
B) The y component of vector is equal to
B
23) Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?
A
24) A boulder rolls off of a very high cliff and experiences no significant air resistance. While it is falling, its trajectory is never truly vertical.
A) True
B) False
B
25) For general projectile motion with no air resistance, the horizontal component of a projectile's velocity
A) remains zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) first decreases and then increases.
A
26) For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration
A) is always zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) first decreases and then increase
B
27) For general projectile motion with no air resistance, the vertical component of a projectile's acceleration
A) is always zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) first decreases and then increases.
E
28) Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice.)
A) The speed of the object is constant but its velocity is not constant.
B) The acce
C
29) A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?
A) It is impossible t
C
30) In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. Compare the times of fall of the two pebbles.
A) The thrown pebble hits first.
B) The dropped pebble hits first.
C) They
B
31) A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will
A) be behind the package.
B) be directly over the package.
C) be in fro
B
32) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below
C
33) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below if the
B
34) A player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory
A) both the velocity and the acceleration of the soccer ball are zero.
B) neither the ball's velocity nor its acceleration are zero.
C) the b
C, E
35) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30� below the horizontal; Debra throws her snowball upward, at 30� above the horizon
A, D
36) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30� below the horizontal; Debra throws her snowball upward, at 30� above the horizon
D
37) A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground? (There co
D
38) You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat
A) directly towa
C
39) You push on box G that is next to box H, causing both boxes to slide along the floor, as shown in the figure. The reaction force to your push is
A) the push of box G on box H.
B) the push of box H on box G.
C) the push of box G against you.
D) the upw
C
40) A small car and a large SUV are at a stoplight. The car has a mass equal to half that of the SUV, and the SUV can produce a maximum accelerating force equal to twice that of the car. When the light turns green, both drivers push their accelerators to
D
41) An object is moving with constant non-zero velocity. Which of the following statements about it must be true?
A) A constant force is being applied to it in the direction of motion.
B) A constant force is being applied to it in the direction opposite o
B
42) A 20-ton truck collides with a 1500-lb car. Which of the following statements must be true?
A) During the collision, the force on the truck is greater then the force on the car.
B) During the collision, the force on the truck is equal to the force on
42 m/s at 31� north of west
1) A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?
D
2) The x component of vector is 8.7 units, and its y component is -6.5 units. The magnitude of is closest to
A) 9.9 units
B) 7.9 units
C) 8.9 units
D) 11 units
E) 12 units
A
3) When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal?
A) 75�
B) 57 �
C) 33�
D) 15�
A
4) When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity?
A) 4.8 m/s
B) 4.3 m/s
C) 3.8 m/s
D) 3.4 m/s
A
5) The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the +x-axis is closest to
A) 340�
B) 160�
C) 250�
D) 110�
E) 23�
+6.6 units and -6.6 units
6) A vector in the xy-plane has an x component of -7.50 units. What must be the y component of this vector so that its magnitude is 10.0 units. (Note: There are two possible answers.)
D
7) A displacement vector is 34.0 m in length and is directed 60.0� east of north. Selecting from the choices in the table below, what are the components of this vector?
Northward Eastward
choice component component
1 29.4 m 17.0 m
2 18.2 m 28.1 m
3 22.4 m
E
8) A player throws a football 50.0 m at 61.0� north of west. What is the westward component of the displacement of the football?
A) 64.7m
B) 55.0 m
C) 0.00 m
D) 74.0 m
E) 24.2 m
(a) 22.6� (b) 13.0 m
9) A vector has components Ax = 12.0 m and Ay = 5.00 m.
(a) What is the angle that vector makes with the +x-axis?
(b) What is the magnitude of vector ?
(a) 5.00 m (b) 53.1�
10) The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively.
(a) What is the magnitude of this vector?
(b) What angle does this vector make with the positive +y-axis.
A
11) A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0� above the horizontal. What is the horizontal component of the boy's velocity?
A) 18.1 m/s
B) 15.6 m/s
C) 8.45 m/s
D) 12.6 m/s
E) 9.33 m/s
A
12) The magnitude of is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 � with the +y-axis. The components of are closest to:
A) = -3.1 m, = 4.6 m.
B) = 3.1 m, = -4.6 m.
C) = 4.6 m, = -3.1 m.
D) = -4.6 m, = 3.1 m.
E) = -4.6 m,
A
13) The components of vectors and are given as follows:
= -9.2 = -4.5
= -6.1 = 4.3
The angle (less than 180�) between vectors and is closest to
A) 77�.
B) 103�.
C) 10�.
D) 170�.
E) 84�.
C
14) A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?
A) 0 km
B) 20 km
C) 28 km
D) 40 km
A
15) You walk to the north, then turn 60� to your right and walk another How far are you from where you originally started?
A) 68 m
B) 39 m
C) 75 m
D) 35 m
A
16) You walk 53 m to the north, then you turn 60� to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east.
A) 63� N of E
B) 50� N of E
C) 57� N of E
D) 69� N of E
A
17) The components of vectors and are given as follows:
Ax = 7.6 Bx = -5.1
Ay = -9.2 By = -6.8
What is the magnitude of the vector difference - ?
A) 13
B) 3.5
C) 16
D) 170
E) 3.4
D
18) If vector has components Ax = -3.0 lb and Ay = -4.0 lb, and vector has components Bx = 3.0 lb and By = -8.0 lb, what is the magnitude of vector = - ?
A) 13 lb
B) 16 lb
C) 140 lb
D) 7.2 lb
A
19) Vector has magnitude 2 units and is directed to the north. Vector has magnitude and is directed to the south. Calculate the magnitude and direction of
A) 7 units, north
B) 7 units, south
C) 3 units, north
D) 3 units, south
C
20) Two perpendicular vectors, and , are added together giving vector . If the magnitudes of both vectors and are doubled without changing their directions, the magnitude of vector will
A) increase by a factor of 8.
B) increase by a factor of 4.
C) increa
6.6 lb at 68� clockwise from rope A
21) Three ropes are tied in a knot as shown in the figure. One student pulls on rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How hard and in what direction must you pull on rope C to balance the first two p
(a) 6.6 (b) 170�
22) The figure shows two vectors and , along with their magnitudes and directions. The vector is given by = - .
(a) What is the magnitude of vector ?
(b) What angle does vector make with the +x-axis?
(a) Ax = 5.5 cm, Ay = 0 cm (b) Bx = -6.5 cm, By = 3.8 cm
(c) Rx = -1.0 cm, Ry = 3.8 cm (d) 3.9 cm at 75� above the -x axis
23) Displacement vector is 5.5 cm long and points along the +x-axis. Displacement vector is 7.5 cm long and points at +30� to the -x-axis.
(a) Determine the x and y components of vector .
(b) Determine the x and y components of vector .
(c) Determine the
(a) Ax = 65 cm, Ay = 38 cm (b) Bx = -25 cm, By = 0 cm
(c) Cx = -28 cm, Cy = -28 cm (d) Rx = 12 cm, Ry = 9 cm
(e) 15 cm at 38� above the +x-axis
24) Displacement vector is 75 cm long and points at 30� above the +x-axis. Displacement vector is 25 cm long and points along the -x-axis. Displacement vector is 40 cm long and points at 45� below the -x-axis.
(a) Determine the x and y components of vecto
A
25) Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by
A) 5.00 m at an angle of 36.9� south of east.
B) 5.00 m at an angle of 53.1� south of east.
C) 5.00 m at an angle of 71.6� south of east.
D) 5.00
D
26) Vector has a magnitude of 6.0 m and points 30� north of east. Vector has a magnitude of 4.0 m and points 30� east of north. The resultant vector + is given by
A) 0.70 m at an angle of 42� north of east.
B) 14 m at an angle of 42� north of east.
C) 1.1
C
27) Vector has a magnitude of 6.0 m and points 30� north of east. Vector has a magnitude of 4.0 m and points 30� west of north. The resultant vector + is given by
A) 9.8 m at an angle of 64� east of north.
B) 9.8 m at an angle of 26� north of east.
C) 7.2
D
28) Vector has a magnitude of 6.0 m and points 30� north of east. Vector has a magnitude of 4.0 m and points 30� west of south. The resultant vector + is given by
A) 2.7 m at an angle of 8.3� south of east.
B) 2.7 m at an angle of 8.3� east of south.
C) 3
A
29) Vector has a magnitude of 6.0 m and points 30� south of east. Vector has a magnitude of 4.0 m and points 30� west of south. The resultant vector + is given by
A) 7.2 m at an angle of 64� south of east.
B) 3.3 m at an angle of 64� south of east.
C) 9.8
D
30) Vector has a magnitude of 4.0 m and points 30� south of east. Vector has a magnitude of 2.0 m and points 30� north of west. The resultant vector + is given by
A) 10.0 m at an angle 30� south of east.
B) 10.0 m at an angle 60� east of south.
C) 2.0 m a
D
31) Vector has a magnitude of 7.0 m and points 30� east of north. Vector has a magnitude of 5.0 m and points 30� west of south. The resultant vector + is given by
A) 10.0 m at an angle 60� north of east.
B) 10.0 m at an angle 30� east of north.
C) 2.0 m a
B
32) Vector has a magnitude of 6.0 m and points 30� east of south. Vector has a magnitude of 4.0 m and points 30� west of north. The resultant vector + is given by
A) 2.0 m at an angle of 30� north of west.
B) 2.0 m at an angle of 30� east of south.
C) 10.
D
33) Vector has a magnitude of 8.0 m and points east, vector has a magnitude of 6.0 m and points north, and vector has a magnitude of 5.0 m and points west. The resultant vector + + is given by
A) 2.0 m at an angle 63� north of east.
B) 2.0 m at an angle 6
C
34) The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to
A) 19
B) 16
C) 13
D) 10
E) 7.0
1.6 lb, 312�
35) Find the magnitude and direction of the resultant of the three force vectors, , , and , shown in the figure. These vectors have the following magnitudes: A = 5.0 lb, B = 7.9 lb, and C = 8.0 lb. Express the direction of the resultant by specifying the
35 m at 39� north of east
36) Two boys, Joe and Sam, who are searching for buried treasure start underneath the same tree. Joe walks 12 m east and then 12 m north, while Sam walks 15 m west and then 10 m south. Both boys then stop. Find the magnitude and direction of the vector fr
A
37) An airplane undergoes the following displacements, all at the same altitude: First, it flies in a direction 30.0� east of north. Next, it flies due south. Finally, it flies 30.0� north of west. Use components to determine how far the airplane ends up
(a) 185 N (b) 77.8� above the +x-axis
38) Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures.
(a) What is the magnitude of the resultant force on the object?
(b) What is the direction of the resultant force
E
39) Three forces, 1, 2, and 3, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is
A) 35 N.
B) 70 N.
C) 140 N.
D) 210 N.
E) 0 N.
D
40) Three forces, 1, 2, and 3, all act on an object, as shown in the figure. The magnitudes of the forces are: F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N. The resultant force acting on the object is given by
A) 180 N at an angle of 60.0� with respect to +x
D
41) Four vectors, , , , and , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction
A) 4.0 cm, along +x-axis.
B) 4.0 cm, along -x-axis.
C) 4.0 cm, along +y-axis.
D) 4.0 cm, along -y-axis.
E) 4.0 cm, 45� above +x
D
42) Vector has a magnitude of 8.0 m and points 30� north of east; vector has a magnitude of 6.0 m and points 30� west of north; and vector has a magnitude of 5.0 m and points 30� west of south. The resultant vector + + is given by
A) 2.7 m at an angle 74�
-11 cm (x component), -4.5 cm (y component)
43) The figure shows three vectors, , , and , having magnitudes 7.0 cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three vectors.
14.4 m
44) The figure shows four vectors, , , , and , having magnitudes 10.0 m, 8.00 m, 6.00 m, and 2.00 m, respectively. Find the magnitude of the sum of these four vectors.
A
45) The figure shows four vectors, , , , and , having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is
A) 16.4 m at an angle 77.8� with respect to +x-axis.
B) 16.4 m at an angle 12.3� with respect to +x-axis.
C)
0.00 cm (x component), 4.2 cm (y component)
46) The figure shows four vectors, , , , and . Vectors and each have a magnitude of 7.0 cm, and vectors and each have a magnitude of 4.0 cm. Find the x and y components of the sum of these four vectors.
4.2 cm along the +y-axis
47) The figure shows four vectors, , , , and . Vectors and both have a magnitude of 7.0 cm, and vectors and both have a magnitude of 4.0 cm. Find the magnitude and direction of the sum of these four vectors.
85 m at 5.4� above the +x-axis
48) The figure shows three vectors, , , and , along with their magnitudes. Determine the magnitude and direction of the vector given by - - .
100 m at 31� above the +x-axis
49) The figure shows three vectors, , , and , along with their magnitudes. Determine the magnitude and direction of the vector given by + - .
E
50) Three vectors, , , and , have the components shown in the table. What is the magnitude of the resultant of these three vectors?
x component y component
3.50 m -4.50 m
2.00 m 0.00 m
-5.50 m 2.50 m
A) 5.50 m
B) 13.0 m
C) 11.1 m
D) 7.00 m
E) 2.00 m
D
51) Three vectors, , , and , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis?
x component y component
-3.5 m 4.5 m
0.00 m -6.5 m
5.5 m -2.5 m
A) 24� above the +x-axis
B) 24� below the +x-a
(a) 20 m (b) 0 m
52) A runner runs on a circular path of radius 10 m. What is the magnitude of the displacement of the jogger if he runs
(a) half-way around the track?
(b) all the way around the track?
18 m/s
53) A player hits a tennis ball into the air with an initial velocity of 32 m/s at 35� from the vertical. How fast is the ball moving at the highest point in its trajectory if air resistance is negligible?
A
54) A ball is thrown with an initial velocity of 20 m/s at an angle of 60� above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory?
A) 10 m/s
B) 17 m/s
C) 20
B
55) A ball is thrown at an original speed of 8.0 m/s at an angle of 35� above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?
A) 4.0 m/s
B) 8.0 m/s
C) 16 m/s
D) 9.8 m/s
D
56) A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligi
C
57) A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?
A) 14 m
B) 16 m
C) 20 m
D) 24 m
C
58) A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?
A) 6.1 m/s
B) 7.4 m/s
C) 8.1 m/s
D) 8.9 m/s
68 m
59) As shown in the figure, a heavy rock is shot upward from the edge of a vertical cliff. It leaves the edge of the cliff with an initial velocity of 15 m/s directed at 25� from the vertical and experiences no appreciable air resistance as it travels. Ho
D
60) The acceleration due to gravity on the Moon is only one-sixth of that on Earth, and the Moon has no atmosphere. If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle) as on Earth, how far would the ball would tra
A
61) A boy throws a rock with an initial velocity of at 30.0� above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2?
A) 0.160 s
B) 0.282 s
C) 0.313 s
D
A
62) A cat leaps to try to catch a bird. If the cat's jump was at 60� off the ground and its initial velocity was what is the highest point of its trajectory, neglecting air resistance?
A) 0.29 m
B) 0.58 m
C) 10.96 m
D) 0.19 m
A
63) A fisherman casts his bait toward the river at an angle of 25� above the horizontal. As the line unravels, he notices that the bait and hook reach a maximum height of What was the initial velocity he launched the bait with? Assume that the line exerts
A
64) A football kicker is attempting a field goal from out. The ball is kicked and just clears the lower bar with a time of flight of If the angle of the kick was 45�, what was the initial speed of the ball, assuming no air resistance?
A) 21.5 m/s
B) 19.7
A
65) You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to
A) 28 m/s
B) 20 m/s
C) 40 m/s
D) 37 m/s
963 m
66) A shell is launched with a velocity of 100 m/s at an angle of 30.0� above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the shell strike the ground? There is no appreciable air resistance,
140 m
67) At target practice, a rifle bullet is fired at an angle of 30� below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below if air resistance is ne
33 m/s
68) A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50� above the horizontal just above ground level, how fast was it hit?
(a) 75.0 cm (b) 0.505 s
69) A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the acceleration due to gravity is 9.80 m/s2.
(a) How far from the base of the table will it strike the floor?
(b) How lo
(a) 0.821 s (b) 267 m
70) A hunter points a rifle horizontally and holds it 3.30 m above the ground. The bullet leaves the barrel at 325 m/s and experiences no significant air resistance. The acceleration due to gravity at this location is 9.80 m/s2.
(a) How long does it take
(a) 25 m (b) 27 m
71) A girl throws a rock horizontally with a speed of 12 m/s from a bridge. It falls 2.28 s before hitting the water below. Neglect air resistance.
(a) How high is the bridge from the water below?
(b) How far horizontally does the rock travel before strik
(a) 19 m/s (b) 31 m/s
72) A celebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground. It hits the ground at a point 60 m from the building without appreciable air resistance.
(a) What will be the horizontal component of the
(a) 12 m/s (b) 25 m/s
73) Enzo throws a rock horizontally with a speed of 12 m/s from a bridge. It falls for 2.28 s before reaching the water below with no appreciable air resistance. Just as the rock reaches the water, find
(a) the horizontal component of its velocity.
(b) th
35 m/s
74) A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligi
A
75) A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect
B
76) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance. The height of the platform above the ground is 2.0 m. What is the magnitude of the vertical compo
D
77) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/shorizontally in a city where the acceleration due to gravity is 9.81 m/s2. The puck experiences no significant air resistance as it falls. The height of the
A
78) A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package, and 2.0 s later it drops a second package. How far apart will the two packages land on the ground if air resistance is negligible?
A) 100 m
B) 160 m
C) 180
B
79) In a room where g = 9.81 m/s2, a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is the speed of the puck just before it hits the ground? The
A
80) A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the horizontal velocity of the ball just before it touche
(a) 3.4 s (b) 78 m (c) vhoriz = 23.4 m/s, vvert = 33 m/s downward
81) A projectile is shot horizontally at 23.4 m/s from the roof of a building 55 m tall and experiences negligible air resistance.
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of t
D
82) A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s
E
83) A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m, as shown in the figure. The width of the pylon is very narrow, and the length of each propeller blade is 12 m. A tip of the propeller breaks off just when the pr
A
84) A boy throws a ball with an initial velocity of 25 m/s at an angle of 30� above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0 s?
A) 5.4 m
B) 13 m
C) 25 m
D) 43 m
E) 50 m
C
85) A projectile is fired from ground level with a speed of 150 m/s at an angle 30� above the horizontal on an airless planet where g = 10.0 m/s2. What is the horizontal component of its velocity after 4.0 s?
A) 150 m/s
B) 35 m/s
C) 130 m/s
D) 75 m/s
E) 3
B
86) A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30� above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected?
A) 150 m/s
B) 36 m/s
C) 130 m/s
D) 75 m/s
E) 38 m/s
45�
87) A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If there was no air resistance, at what angle above the horizontal did it leave the ground?
B
88) A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.0 m/s at an angle of 40� above the horizontal. The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high. The ball just clears the fence while s
B
89) A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30� above the horizontal. What is the horizontal distance to the point where the football hits the ground if we neglect air resistance?
A) 20 m
B) 35 m
C) 18 m
B
90) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55� with the vertical. What is the length of the athlete's jump if air resistance is of no significance?
A) 0.88 m
B) 8.0 m
C) 12 m
D) 17 m
E) 4.0 m
C
91) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35� above the horizontal. How long does the athlete stay in the air, assuming no significant air resistance?
A) 0.50 s
B) 0.88 s
C) 1.1 s
D) 2.5 s
E) 0.54
C
92) An athlete participates in an interplanetary discus throw competition during an Olympiad that takes place on a planet where the acceleration due to gravity is 9.7 m/s2. He throws the discus with an initial velocity of 20 m/s at an angle of 60� from th
(a) 7.5 m (b) 1.2 s (c) 9.1 m/s
93) A child throws a ball with an initial speed of 8.0 m/s at an angle of 40� above the horizontal. The ball leaves her hand 1.0 m above the ground and experiences no appreciable air resistance as it moves.
(a) How far from where the child is standing doe
C
94) A child throws a ball with an initial speed of 8.0 m/s at an angle of 40� above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground?
A) 35�
B) 42�
C) 48�
D) 40�
E) 65�
B
95) The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. If there is no air resistance, how long does it take the football to reach the top of its trajectory?
A) 1.0 s
B) 2.0 s
C) 3.0 s
D) 4.0 s
C
96) A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal?
A) 45�
B) 60�
C)
B
97) A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the pro
(a) 3.7 s (b) 68 m (c) vhorizontal = 42 m/s, vvertical = 0 m/s
(d) ahorizontal = 0 m/s2, avertical = -9.8 m/s2
98) A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of 41.2� above the horizontal. Neglect air resistance, take upward as the positive direction, and use g = 9.8 m/s2.
(a) Determine the time necessary for the projecti
27.4 m/s
99) At a location where g = 9.80 m/s2, a projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed?
96 m
100) A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30� above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air
10 m/s
101) A 5.0-kg stone is thrown upward at 7.5 m/s at an angle of 51� above the horizontal from the upper edge of a cliff, and it hits the ground 1.5 s later with no air resistance. Find the magnitude of its velocity vector just as it reaches the ground.
(a) 67 m/s (b) 340 m (c) 190 m
102) A projectile is thrown upward at 24� with the vertical and returns to the horizontal ground 12.5 s later with no air drag.
(a) How fast was it thrown?
(b) How far from its original position did it land?
(c) How high above its original position did it
B
103) A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal) and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q.
A
104) As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of and The projectile rises and then falls into the sea at point P. The time of flight of the projectile is
D
105) A projectile is launched with an initial velocity of 80 m/s at 30� above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration?
A) 80 m/s2
B) 40 m/s2
C) 9.8 m/s2
D) 0 m/s2
E) 69 m/s2
C
106) A boy kicks a football with an initial velocity of 20 m/s at an angle of 25� above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is
A) 25 m/s2.
B) 18 m/s2.
C) 9.8 m/s2.
D) 8.5 m/s2.
D
107) A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance,
A) its range will be increased by .
B) its range will double.
C) its range will be decreased by a fac
A
108) A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s2?
A) 69.0�
B) 67.4
B
109) You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is
A) -10 mi/h.
B) 10 mi/h.
C) 65 mi/h.
D) 35 mi/h.
A
110) Your motorboat can move at 30 km/h in still water. What is the minimum time it will take you to move 12 km downstream in a river flowing at 6.0 km/h?
A) 20 min
B) 22 min
C) 24 min
D) 30 min
120 km/h
111) An airplane with an airspeed of 140 km/h has a heading of 50� west of north in a wind that is blowing toward the east at 25 km/h. What is the groundspeed of the plane?
C
112) A plane has an airspeed of 200 m/s northward, and is in a wind of 50.0 m/s to the west. The plane's speed relative to the ground is
A) 150 m/s.
B) 200 m/s.
C) 206 m/s.
D) 250 m/s.
B
113) An airplane with an airspeed of 120 km/h has a heading of 30� east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground?
A) 90 km/h
B) 110 km/h
C) 140 km/h
D) 150 km/h
A
114) A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0� below the horizontal. At that instant, what is the speed of the projectile with respect to a stationary observer on the ground?
A) 245 m/s
B) 250 m/
61�
115) Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal?
B
116) On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race?
A) 250 s
B) 750
20 m/s at 15� east of south
117) A pickup truck moves at 25 m/s toward the east. Ahmed is standing in the back and throws a baseball in what to him is the southwest direction at 28 m/s (with respect to the truck). A person at rest on the ground would see the ball moving how fast in
11 m/s at 63� north of east
118) A submarine must travel how fast (with respect to the water) and be pointed in what direction such that it moves 10 m/s directly northward (relative to the earth) if the water moves westward at 5.0 m/s?
94 m/s at 32� north of east
119) An airplane is pointed at 45� north of east and is moving at 71 m/s with respect to the air. The jet stream (moving air) carries the plane at 30 m/s toward the east. What are the magnitude and direction of the velocity of the plane relative to the gr
(a) 60� (b) 3.1 min
120) The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river in which the current flows at 5.0 m/s.
(a) At what angle, measured from the upstream direction, should the driver head the boat?
(b) How many mi
(a) Alice (b) Alice arrives 110 s before John
121) A 960-m wide river flows at 16 m/s as shown in the figure. Alice and John have a race in identical boats which each travel 20 m/s in still water. Alice leaves point A and steers so that she goes straight to point B directly across and then back to A.
A
122) A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is
A) 157 m/s at an angle 7.31� south of east.
B) 157 m/s at a
D
123) A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative to the ground?
A) 78.1� north of east
B) 11.9� north o
D
124) A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?
A) 130 m/s
B) 16 m/s
C)
A
125) An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the point of origin of the flight. The plane flies with an airspeed of 120 m/s. If a constant wind blows at 10 m/s toward the west during t
A
126) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water?
A) 0.50 m/s
B) 0.80 m/s
C) 1.2 m/s
D) 1.4 m/s
E) 1.8 m/s
C
127) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current?
A) 0.50 m/s
B) 0.80 m/s
C) 1.2 m/s
D) 1.4 m/s
E) 1.8 m/s
(a) 0.775 m/s (b) 1.57 m/s
128) A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3� (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) What is the speed of the current?
(b) What is the resultant
D
129) A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing on the shore as it crosses the river?
A) 5.3 m/s
A
130) A plane flies directly from city A to city B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes less than the trip from A t
A
131) The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in the pulley, and the connecting rope is very
(a) 60,000 N (b) 35,000 N
132) A locomotive is pulling three train cars along a level track with a force of 100,000 N. The car next to the locomotive has a mass of 80,000 kg, the next one, 50,000 kg, and the last one, 70,000 kg. You can neglect the friction on the cars being pulle
C
133) In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long d
160 N
134) A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force must be applied to the box to cause it to start sliding alon
B
135) The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is applied to the box?
A) 12 N
B) 8.8 N
C) 15 N
D) 6.0
A
136) An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s2. What is the coefficient of kinetic friction between the object and the floor?
A) 0.24
B) 0.48
C) 0.12
D) It is impossible to determine
220 N
137) A bulldozer attempts to drag a log weighing 500 N along the rough horizontal ground. The cable attached to the log makes an angle of 30� above the ground. The coefficient of static friction between the log and the ground is 0.50, and the coefficient
B
138) A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came
D
139) A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force must be exerted on the box for it to accelerate
C
140) A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0� below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic fricti
B
141) A baseball player is running to second base at 5.03 m/s. When he is 4.80 m from the plate he goes into a slide. The coefficient of kinetic friction between the player and the ground is 0.180, and the coefficient of static friction is 3.14. What is hi