Two-Dimensional Motion

Two-Dimensional Motion Projectile Motion – A projectile is any object that is thrown into the air. Zero Launch Angle General Launch Angle

A child rides on a pony walking with constant velocity A child rides on a pony walking with constant velocity. The boy leans over to one side and a scoop of ice cream falls from his ice cream cone. Describe the path of the scoop of ice cream as seen by (a) the child and (b) his parents standing on the ground nearby.

Independence of Vertical and Horizontal Motions

At the instant a horizontally held rifle is fired over a level range, a bullet held at the side of the rifle is released and drops to the ground. Which bullet—the one fired horizontally or the one dropped from rest—strikes the ground first? Answer: Same time. Time Lapse Photo

Ball A rolls at a constant speed of 0. 25 m/s on a table 0 Ball A rolls at a constant speed of 0.25 m/s on a table 0.95 m above the floor, and ball B rolls on the floor directly under the first ball and with the same speed and direction. When ball A rolls off the table and hits the floor, (a) ball B is ahead of ball A, (b) ball B collides with ball A, or (c) ball A is ahead of ball B. Why? Answer: (b) ball B collides with ball A

If you are carrying a ball and running at constant speed and wish to throw the ball so that you can catch it as it comes back down, should you (a) throw the ball at an angle of about 45o above the horizontal and maintain the same speed, (b) throw the ball straight in the air and slow down to catch it, or (c) throw the ball straight in the air and maintain the same speed? Answer: (c) throw the ball straight up and maintain the same speed.

Zero Launch Angle

A home run is hit in a baseball game A home run is hit in a baseball game. The ball is hit from home plate into the center field stands, along a parabolic path. What is the acceleration of the ball (a) while it is rising, (b) at the highest point of the trajectory, and (c) while it is descending after reaching the highest point? Ignore air resistance. Answer: - 9.81 m/s2 the entire time

Two divers run horizontally off the end of a diving board Two divers run horizontally off the end of a diving board. Diver 2 runs with twice the speed of diver 1. When the divers hit the water, is the horizontal distance covered by diver 2 (a) the same as, (b) twice as much as, or (c) four times the horizontal distance of diver 1? Answer: (b) twice as much

Answer: (a) greater than

Answer: (b) decrease

General Launch Angle

When jumping to score, basketball players seem to be suspended momentarily, or to “hang” in the air. Explain the physics of this effect.

Answer: (c) the same

Maximum Range and Symmetry with Launch Angles

Three projectiles (a, b, and c) are launched with the same initial speed but with different launch angles, as shown in Figure 4-12. List the projectiles in order of increasing (a) horizontal component of initial velocity and (b) time of flight. Answer: (a) ax > bx > cx (b) c > b > a

Concept Test: A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? 1. A 2. both at the same time 3. B 4. need more information Answer: Enemy ship B gets hit first.

As a projectile moves in its parabolic path, the velocity and acceleration vectors are perpendicular to each other (a) everywhere along its path, (b) at the peak of its path, (c) nowhere along its path, or (d) not enough information is given. Answer: (b) at the peak [see next slide]

Concept Test: Consider the situation depicted here Concept Test: Consider the situation depicted here. A gun is accurately aimed at a dangerous criminal hanging from the gutter of a building. The target is well within the gun’s range, but the instant the gun is fired and the bullet moves with a speed vo, the criminal lets go and drops to the ground. What happens? The bullet Hits the criminal Misses and goes above the criminal. 3. Misses and goes below the criminal. Answer: 1. hits the criminal

Bart Simpson attempts a jump: If his horizontal velocity is 15m/s does he make the jump? Yes No 0.5m 4.0m