A ball is dropped vertically, falls through a height h and strikes a ramp that is inclined 45 degrees to the horizontal. The ball undergoes perfectly elastic collision.
(a) How far down the ramp does the ball land after the first bounce?
(b) Calculate the time \(t\) between the first bounce and the second bounce.
(c) Calculate the speed of impact, \(v_0\) and the angle \(\theta\) that the ball makes with the vertical at the second impact.
(d) For the second and third bounces, find the distance the ball travels down the ramp (in term of \(h\)), the time in the air (in terms of \(t\)), and the speed at impact (in term of \(v_0\)) and the tangent of the angle with the vertical at impact.
(e) Generalize your answers to the nth bounce for the quantities in part (e).