1. Projectile Motion
AP Physics C

2. What is projectile?
Projectile – an object that is acted on by only a gravity

3. Projectiles move in TWO dimensions
Horizontal and Vertical motion

4. Combining the Components
Together, these components produce what is called a trajectory or path. This path is parabolic in nature.
Component
Magnitude
Direction
Horizontal ?
Vertical

5. Horizontal “Velocity” Component
NEVER changes
Why does the horizontal velocity never change?

6. Vertical “Velocity” Component
Changes (due to gravity), does NOT cover equal displacements in equal time periods.
How does the magnitude and direction of vertical velocity change?

7. Horizontally Launched Projectiles
Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.

8. Horizontally Launched Projectiles
To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #2.
x =
y =

9. Horizontally Launched Projectiles
Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?
What do I know?
What I want to know?
10.1 seconds, 1010 m

10. Example 1
A rock is thrown horizontally from a m high cliff. It strikes a level ground 90.0 m from the base of a cliff. At what speed is it thrown?
19.9m/s

11. Example 2 A tiger leaps horizontally from a
15 m high rock with a speed of 7.0 m/s. How far from the base of the rock will it land?
12.24 m

12. Example 3
An arrow is fired horizontally with a speed of 10 m/s and travels a horizontal distance of 6m. How far does it fall vertically?
1.8m

13. Example 4
A boy throws a pebble horizontally with speed 12 m/s from a bridge that is 8.0 m above the water.  (a) How much time is the pebble in the air?  (b) How far is the pebble from the boy when it splashes?  (c) What is the speed of the pebble when it hits the water?
a. 1.3 s b. 17 m (8 m down, 15 m over) c. 17 m/s

14. Example 5
A ball is thrown horizontally from the top of a cliff with initial speed v0. At any moment its direction of motion makes an angle Ɵ to the horizontal. Derive a formula for Ɵ as a function of time.
Tan^-1(10t/vo)

15. Example 6
A stone is thrown from the top of a building horizontally with an initial speed of 20 m/s. The height of the building is 45 m.
a) How long does it take the stone to reach the ground?
b) What is the speed of the stone just before it strikes the ground? 3s
36 m/s