Projectile
An object with independent vertical and horizontal motions that move through the air only under the force of gravity after the initial thrust
Examples of projectile motion
Football or bullet
What do you ignore in projectile motion
Air resistance
Trajectory
The path of a projectile through space
If you know the initial velocity, you can find
The projectile's trajectory
Two ways projectiles can be launched
Horizontallly or at an angle
How does gravity affect the trajectory
Gravity curves trajectory downward along a parabolic path
Two types of motion
Horizontal and vertical
Projectiles launched horizontal: Initial horizontal velocity (Vxi)=
Initial velocity of projectile (Vi)
Projectiles launched horizontal: Horizontal motion- acceleration
0 m/s2
Projectiles launched horizontal: Horizontal motion - velocity
Constant
Projectiles launched horizontal: Vertical motion- velocity
No initial velocity (Vyi= 0 m/s2
Projectiles launched horizontal: Vertical motion- acceleration
-9.80 m/s2
What type of acceleration in vertical motion
Uniform
Projectiles launched at an angle : Components of initial velocity
Horizontal and vertical
Projectiles launched at an angle- If the object is launched upward, then it
Rises with slowing speed, reaches top of path and descends with increasing speed
Projectiles launched at an angle: horizontal- intial horizontal velocity (Vxi)
Vxi= Vixcostheta
Projectiles launched at an angle: horizontal- acceleration
0 m/s2
Projectiles launched at an angle: horizontal- velocity
Constant
Projectiles launched at an angle: vertical- initial vertical velocity (Vyi)
Vyi= given number costheta
Projectiles launched at an angle: vertical- acceleration
-9.80 M/s2- uniform
Projectiles launched at an angle- Formula for Vyi
Vyi= Vix sin theta
Projectiles launched at an angle- 3 ways the trajectory can be described
Maximum height, range, flight time
Maximum height
The height of the projectile when the vertical velocity is zero
Range (R)
The horizontal distance the projectile travels
Flight time
The time the projectiles in the air
What is flight time also called
Hang time
To solve motion in two dimensions
Break the problem into two one dimensional motion problems
Steps to solve motion in two dimensions- vertical
1. Vertical motion
- think of object being dropped or thrown straight into air
- gravity force acts on object accelerating it by 9.80 m/s 2
Steps to solve motion in two dimensions- horizontal
- Constant velocity problem
- no thrust force, drag is neglected
- no acceleration- no horizontal direction
How are vertical and horizontal motion connected
Variable time- the time is the same
What is the same for verticl and horizontal motion
Time for launch of projectile to time it hits target
Is time for both dimensions the same
Yes- solving for one dimension is the time for other dimension
Effect of forces due to air
Change the motion of object
Uniforms circular motion
The movement of an object at a constant speed around a circle fixed radius
Example of uniform circular motion
Person on merry go round or sock in washer
An object moving in a circle at constant speed is
Accelerating toward the center of the circle
Uniform circular motion: Even though speed is constan objetc is still.
Accelerating due to the change in direction
Can an object be accelerating if velocity is constant?
Yes- velocity is a vector, change in direction is accelerating
Centripetal acceleration
The center seeking acceleration of an object moving in a circle at constant speed
What does centripetal mean
Center seeking
Centripetal acceleration- to describe the velocity of an object moving in a circle ,
You need to knwo the circumference of the circle and period of motion
Centripetal acceleration- what is the period
Time need for object to make one complete revolution
Velocity formula
V= 2pi(r)/T
Formula for centripetal acceleration
Ac= v2/r
Formula for centripetal force
Fc= m *ac or FC = fnet
Centripetal force
the net force exerted toward the center of the circle that causes an object to have a centripetal acceleration
What does the agent of centripetal force depend on
The situation
Examples of centripetal force
Friction and tension
What does the object's velocity depend on
The reference frame chosen
Reference frame
A coordinate system from which motion is viewed
How can an object's velocity be described
Relative to another objetc's velocity
Relative velocity in one dimension - add
You add the velocities if they are in the same direction
Relative velocity in one dimension- Subtract
You should subtract the velocities if they are in opposite directions
Relative velocity. In two dimensions-
Use vector resolution and addition to solve
What is centripetal acceleration directly proportional to
Velocity
High acceleration
Short radius
Low accelration
High radius
Centripetal acceleration and radius
Inversely related
Direction of acccleration is the same as
Direction of net force
Where does the net force act
Toward the circle
What is centrifugal force
Nonexistent and fictions- no agent- due to inertia