Projectile motion 2-dimensional motion of an object launched non-vertically Falls freely (neglect air resistance unless I tell you otherwise)

Imagine shadow of ball on the wall…. …on the ground Only y motion has acceleration, force Imagine shadow of ball on the wall…. …on the ground

P1. Bob is loading his gun while Fred suddenly shoots his gun horizontally. Bob drops his bullet the instant Fred fires. Whose bullet hits the ground first (from same height)? a. Bob’s b. Fred’s c. at same time Demo: monkey-hunter

x and y motions are connected by the time it takes to complete the path! Hints for projectile motion: Draw pictures, label variables. Decide +y direction Determine initial velocity components If t is not given, identify which coordinate motion has the information to give the total free-fall time, and find t. Find other needed quantities from kinematic eqns.

In this example, the time in the air is the same as that of a ball____ A rock is ejected at an angle of 35o above horizontal, at 25 m/s, from a 20 m high volcano. How far from the volcano does it land? In this example, the time in the air is the same as that of a ball____ rolled at 25 m/s along the ground for 20 m thrown vertically at 25 m/s, hitting the ground 20 m below thrown vertically at 25cos(35) m/s, hitting the ground 20 m below thrown vertically at 25sin(35) m/s, hitting the ground 20 m below dropped vertically, hitting the ground 20 m below

In this example, the time in the air is the same as that of a ball____ rolled at 20 m/s along the ground for 50 m rolled at 20cos(40) m/s along the ground for 50 m rolled at 20sin(40) m/s along the ground for 50 m thrown vertically at 20cos(40) m/s, hitting the ground 50 m below thrown vertically at 20sin(40) m/s, hitting the ground 50 m below

In this example, the time to fall is the same as that of a ball that ….

Find final velocity components   Final speed Final velocity angle

P2. A battleship simultaneously fires two shells at enemy ships P2. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? A. A B. B C. same

P3. Which spends the longest time falling? Sally and Bob each throw a rock horizontally from a cliff. Sally throws her rock hard. Bob throws his more easily.   P3. Which spends the longest time falling? A. Sally’s B. Bob’s C. same P4. Which rock is going fastest (vector magnitude) just before it hits the ground? P5. Sally throws a rock horizontally from a cliff. Bob throws his at an angle above horizontal. They throw the same speed. Which hits first?

P6. A man on a moving railroad car shoots exactly vertically at a bird which is directly over him and moving at the same constant horizontal velocity (no air resistance) His shot will go behind the bird He will hit it His shot will go ahead of the bird

What happens if he misses?

Lecture 4, projectiles Basic concepts: Basic problems, skills: x and y motion are independent, except connected by time x motion is that of a ball moving at constant speed y motion is that of a ball thrown up, down or dropped along y Basic problems, skills: horizontal launching deciding when x or y motion determines when freefall ends Advanced concepts: effect of initial vy Advanced problems, skills: nonhorizontal launching finding final v from components solving when vi or q is not given