calc series question?

Question

A certain ball has the property that each time it falls from a height 'h' onto a hard, level surface, it rebounds to a height 'rh', where 0 < r < 1. Suppose that the ball is dropped from an initial height of 'H' meters.

a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels. (Use the fact that the ball falls 1/2gt^2 meters in 't' seconds)

b) calculate the total time that the ball travels.

c) suppose that each time the ball strikes the surface with velocity 'v' it rebounds with velocity '-kv', where 0 < k < 1. How long will it take for the ball to come to rest?

explanation/steps plz..thanks :)

Answer 1

a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels.

Each time the ball is dropped from a height h, it rebounds to a height rh, 0 < r < 1.

After the initial drop the distance travelled by each rebound is doubled when it hits the groud again. Total distance traved is:

d = h + 2h(r + r² + r³ + ... ) = h + 2h[r/(1 - r)] = h + 2hr/(1 - r)