A relatively elastic ball is thrown from the top of a building to eventually bounce once off of the concrete sidewalk, only to then collide with a region of sticky tape coating a more distant location of the sidewalk, as shown in the figure below. Some facts are known about the process. The ball is initially thrown at an angle, = 30.0, above the horizontal, but at an unknown speed. The height of the building is H = 10.0 m. The vertical speed of the ball is the only component that is altered during the bouncing event, and its vertical speed immediately after the bounce is 40% of the vertical speed immediately before the bounce. The amount of horizontal distance covered by the ball after the bounce is D = 5.0 m. During the bouncing process, the ball is in contact with the concrete for 0.030 s. For the parts that follow, show all of your work and reasoning while adopting a clearly defined coordinate system. (a)  Determine the speed with which the ball was initially thrown.  (b)  Determine the ratio of the horizontal range of the ball before the bounce to the horizontal range of the ball after the bounce.  (c)  Determine the ratio of the maximum height reached by the ball before the bounce to the maximum height reached by the ball after the bounce (both measured relative to the ground).

A relatively elastic ball is thrown from the top of a building to eventually bounce once off of the concrete sidewalk, only to then collide with a region of sticky tape coating a more distant location of the sidewalk, as shown in the figure below. Some facts are known about the process.

The ball is initially thrown at an angle, = 30.0, above the horizontal, but at an unknown speed.

The height of the building is H = 10.0 m.

The vertical speed of the ball is the only component that is altered during the bouncing event, and its vertical speed immediately after the bounce is 40% of the vertical speed immediately before the bounce.

The amount of horizontal distance covered by the ball after the bounce is D = 5.0 m. During the bouncing process, the ball is in contact with the concrete for 0.030 s.

For the parts that follow, show all of your work and reasoning while adopting a clearly defined coordinate system.

1. (a)  Determine the speed with which the ball was initially thrown. 

2. (b)  Determine the ratio of the horizontal range of the ball before the bounce to the horizontal range of the

   ball after the bounce. 

3. (c)  Determine the ratio of the maximum height reached by the ball before the bounce to the maximum height

   reached by the ball after the bounce (both measured relative to the ground). 

4. (d)  Determine the average acceleration vector of the ball during the bouncing process.