A ball is dropped with a velocity v0 at an angle a with the vertical onto the top step of a flight of stairs consisting of 8 steps. The ball rebounds and bounces down the steps as shown. Each time the ball bounces, at points A, B, C, . . . , the horizontal component of its velocity remains constant and the magnitude of the vertical component of its velocity is reduced by k percent. Use computational software to determine (a) if the ball bounces down the steps without skipping any step, (b) if the ball bounces down the steps without bouncing twice on the same step, (c) the first step on which the ball bounces twice. Use values of v0 from 1.8 m/s to 3.0 m/s in 0.6-m/s increments, values of a from 18 ° to 26 ° in 4 ° increments, and values of k equal to 40 and 50.