What are the two ways in which vectors can be described?
-method 1: size and direction
-method 2: components
What does size and direction include?
-magnitude of the vector plus a degree measurement
What do components include?
-the x and y components of the vector
Can (+) and (-) used to be describe the components of a vector?
-yes
Can (+) and (-) ever be used to describe a vector as a whole?
-no
-the direction of a vector is described using degrees
What is the first step to forming a vector using x and y components?
-put the x component and the y component head to tail
And then?
-assemble vector as a whole by connecting the tail of the first vector to the head of the second vector
If a ball is fired from resting, how much velocity is directed in the y direction?
-none of the velocity
How much velocity is directed in the x direction?
-all of it
How much acceleration does gravity cause in the x direction?
-none
-when the x axis is chosen to be horizontal and the y axis points vertically upward, it follows that the acceleration of an ideal projection a(x) = 0
How much acceleration does gravity cause in the y direction?
-when the x axis is chosen to be horizontal and the y axis points vertically upward, it follows that the acceleration of an ideal projection a(y) = -g
What is the basis of solving 2D problems?
-we treat x and y independently
What is flight time typically determined by in 2D kinematic problems?
-the y direction
Of the five values that are used in the constant acceleration equations, which will be the same for both the x and y components?
-only time
Why?
-even though x and y are independent, they describe motion in the same timescale
Is velocity final typically an x or a y question?
-it is both an x and y question
Why?
-because objects will run "diagonally" into the ground
What component is often the delimiting factor for flights?
-the y component
Two people dive off an overhang into a lake. Diver 1 drops straight down, diver 2 runs off the cliff with an initial horizontal speed. Is the splashdown speed of diver 2 greater than, less than, or equal to the splashdown speed of diver 1?
-the speed of diver 2 is greater than diver 1
Why?
-neither diver has an initial component of velocity, and they both fall with the same vertical acceleration (acceleration due to gravity)
-therefore, the two divers fall for the same amount of time, and their y components of velocity are the same at splas
When an object is launched on level ground, what launch angle results in the maximum distance from the launch point?
-45 degrees
What occurs when the angle is less than 45 degrees?
-a smaller range results
Why?
-velocity in the x direction is too large
-object does not have enough hang time
What occurs when the angle is greater than 45 degrees?
-a smaller range results
Why?
-velocity in the y direction is too large
-object does not have enough forward velocity in the x direction
What is the only velocity component of a vector that is present at the top of a flight?
-the x velocity component
What is the acceleration of a projectile when it reaches its highest point?
-equal to (-) g at all times
A projectile is launched with an initial velocity of 4 m/s in the x direction and 3 m/s in the y direction. What is the velocity of the projectile when it reaches its highest point?
- equal to 4 m/s in the x direction
Why?
-at the highest point, the projectile is only moving horizontally
-this means that gravity has reduced its y component of velocity to zero
-the x component is unchanged by the acceleration of gravity
Do projectiles for which air resistance is non-negligible have a maximum range when the launch angle is greater than, less than, or equal to 45 degrees?
-when the launch angle is less than 45 degrees
Why?
-with a smaller launch angle, the golf ball is in the air for less time, giving air resistance less time to affect its flight
A child rides on a pony walking with constant velocity. A scoop from the child's ice cream falls from his cone. What is the path of the scoop as seen by the child?
-the scoop falls straight down
As seen by the parents?
-the scoop follows a parabolic path
As you walk down the street, you toss a ball into the air. If you want the ball to land in your hand when it comes down, should you toss the ball straight up, in a forward direction, or in a backward direction?
-straight up
Why?
-you and the ball have the same horizontal component of velocity
-therefore, the ball will come down in your hand if you throw it straight upward relative to yourself
Two divers run horizontally off of a low cliff. Diver 2 runs with twice the speed of diver 1. When the divers hit the water, is the horizontal distance covered by diver 2 the same as, twice as much as, or four times the horizontal distance covered by dive
-diver 2 covers twice the distance
Why?
-the divers are in free fall for the same amount of time
A penguin jumps out of water onto an ice floe. Just before it lands, is its speed greater than, less than, or the same as when it left the water?
-less than when it left the water
Why?
-since the ice floe is above the water, gravity had an opportunity to chip away at the y component of the penguin's velocity
Suppose that a person is in an elevator rising with constant acceleration. If a person tosses a coin, would the coin's flight time be greater than, less than, or the same as when the person was at rest?
-the coin's time will be less than when the person was at rest
Why?
-the coin has greater acceleration relative to the floor of the elevator, and hence it will reach the floor in less time
Child 1 throws a snowball horizontally from the top of a roof; child 2 throws a snowball straight down. Once in flight, is the acceleration of the snowball 2 greater than, equal to, or less than the acceleration of snowball 1?
-equal to
Why?
-the x acceleration of both objects once in flight is equal to zero
-the y acceleration of both objects once in flight is equal to (-)g
An object is accelerating downward. Which of the following must be true? 1. The object cannot be moving upward. 2. The object cannot be moving in a straight line. 3. The object is moving directly downward. 4. If the object's motion is instantaneously hori
-if the object's motion is instantaneously horizontal, it can't continue to be so
Why?
-instantaneously, velocity and acceleration are independent
-however, if initial velocity is horizontal, acceleration will make it go downwards
Two people dive off a cliff into the lake below. Diver 1 drops straight down, diver 2 runs off the cliff with an initial horizontal speed. Just before entering the water, is diver 2's speed greater than, less than, or equal to the speed of diver 1?
-speed if a vector quantity that is determined by its x and y components. If diver 2's x component is greater than diver 1's x component (while their y components are the same), then his speed upon entering the water will be greater than the speed of dive
A mountain climber encounters a crevasse of width w but the opposite side is a distance h lower. If the distance h were increased but the width remains the same, the minimum horizontal speed needed to jump the crevasse will increase, decrease, or stay the
-decrease
Why?
-initially it might appear that changing delta y has no effect on velocity required in the x direction
-however, the connection point is time
-if the distance between the crevasse is increased, the the climber has more time to travel in the x direction
-t
A cannonball is fired with an initial velocity. At what angle should the cannon be positioned with respect to the horizontal to maximize the time that the cannonball spends in the air?
-90 degrees
Why?
-because sin theta is largest when theta equals 90 degrees
At what angle should the cannon be positioned with respect to the horizontal to maximize the distance of the cannonball?
-zero degrees
Why?
-because cos theta is largest when theta equals zero degrees
A cannon fires a cannonball with initial speed v that reaches a maximum height h. If the initial speed is doubled, the maximum height of the cannonball will be?
-4h
If the initial speed is doubled, the time spent in the air?
-doubles
Increasing the x component of velocity of the cannonball will have what effect on the horizontal range and maximum height of the cannonball?
-horizontal range will increase
-there will be no impact on maximum height
What component of velocity does height depend upon?
-the y component of velocity
What component of velocity does horizontal range depend upon?
-the x component of velocity
Often times, what does horizontal distance travelled depend upon?
-flight time
What is flight time set by?
-y direction
Why?
-when an object returns to the same height, the flight is over