1. Projectile Motion

2. Projectile Motion…
Projectile – objects that are thrown or launched into the air and are subject to gravity
Trajectory – the path that a projectile follows when launched into the air. Parabolic!

3. What factors affect the trajectory of a projectile?
Velocity of launch
Acceleration of gravity
Angle at launch
Air resistance

4. Projectile Launched Horizontally
Vertical motion of a projectile:
Δy = v0y Δt + ½ ay (Δt)2 = -½ g (Δt)2
vy = v0y + ay Δt = -g Δt
vy2 = -2g Δy
Horizontal motion of a projectile:
Δx = v0x Δt + ½ ax (Δt)2 = v0x Δt
vx = v0x = constant

5. Sample Problem 1
A movie director is shooting a scene that involves dropping a stunt dummy out of an airplane and into a swimming pool. The plane is 10.0m above the ground, traveling at a velocity of 22.5 m/s in the positive x direction. The director wants to know where in the plane’s path the dummy should be dropped so that it will land in the pool.
22.5 m/s
22.5 m/s
10.0m

6. Refresh your memory….
A football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial speed of 5.00 m/s.
In the absence of air resistance, how high does the coin go above its point of release?
What is the total time the coin is in the air before returning to its release point?
What is its velocity when it returns to the release point? How does this compare to its initial velocity?

7. Projectile Launched at an Angle
Vertical motion of a projectile:
Δy = v0 (sin θ) - ½ g (Δt)2
vy = v0 (sin θ) - g Δt
vy2 = v02(sin θ)2 - 2g Δy
Horizontal motion of a projectile:
vx = v0 (cos θ) = constant
Δx = v0 (cos θ) Δt

8. Sample Problem 2
A quarterback throws the football to a receiver who is 31.5m down the field. If the football is thrown at an initial angle of 40.0˚ to the ground, at what initial speed must the quarterback throw the ball? What’s the ball’s highest point during the flight?
31.5 m
40˚
vi = ?

9. Monkey and the Coconut ?

10. Do they make it across?
1 mph = m/s Δx θ