1. Projectiles
AP Physics C Mrs. Coyle

2. Horizontal Projectiles are launched with a horizontal initial velocity.

3. Motion in Two Dimensions

4. A horizontal projectile from the same height
Which falls first?
A free falling object Or
A horizontal projectile from the same height

5. A horizontal projectile
Which falls first?
A horizontal projectile Or
A horizontal projectile from the same height with a higher initial horizontal speed

6. Question
A zoologist is aiming at a monkey with a tranquilizer gun. Both are at the same level. The monkey is about to jump. Should the zoologist aim horizontally or low in order to tranquilize the monkey?

7. Horizontal Projectiles
Two dimensional motion
Initial velocity,vx ,is entirely horizontal
X-axis : constant velocity
Y-axis : constant acceleration

8. A Look at the Velocities
Vx= constant
Vyi=0
Vy = a t

9. Characteristics of Path
Trajectory
Parabola
Range

10. Equations for Horizontal Projectiles
x=vx t
____
y= 1 at  t= √2y/a 2
vY=at

11. Projectiles at an Angle

12. Projectiles at an Angle

13. Projectiles at an Angle
Motion in two dimensions
x-axis constant velocity
y-axis constant acceleration
Parabolic trajectory

14. Initial Velocity
vxi=vcosq
vyi=vsinq v

15. A Look at the Velocities

16. Equations for Projectiles at an Angle
Initial Velocity is at an angle with the horizontal
vx=constant
vy=vyi+at a or g=-9.8m/s2
Dy=vyit+ 1at2 2

17. Complementary angles have the same range.

18. Additional Key Points At the max height: vy=0
The entire trip vx=constant=vxi
Maximum range when q=45o in the absence of air resistance.
Complementary angles result in the same range.
Symmetry
Resultant velocity is tangent to the curve at the point of study.
Ignore air resistance.

19. Prove the maximum height equation (for full symmetric motion)

20. Prove the range equation
Hint: Use the identity sin2θ=2sinθcosθ
Why does max range occur at 45o?

21. Non symmetric projectile
Ex: Find t and vf.
Ans: 4.22s, 35.9m/s