Question

10. When a rubber ball is dropped from a height, h cm on to a flat concrete floor, it rebounds to 3 5 h cm a height of Given a rubber ball is dropped from a height of 120cm. Find a) the maximum height achieved by the ball after 2 bounces b) the total distance travelled by the ball when it hits the floor for 10 ^ m times. c) the total distance travelled by the ball if the ball continues to bounce in the same way indefinitely.​

Answer 1

Explanation:

Let the height above which the ball is released be H

This problem can be tackled using geometric progression.

The nth term of a Geometric progression is given by the above, where n is the term index, a is the first term and the sum for such a progression up to the Nth term is

To find the total distance travel one has to sum over up to n=3. But there is little subtle point here. For the first bounce ( n=1 ), the ball has only travel H and not 2H. For subsequent bounces ( n=2,3,4,5...... ), the distance travel is 2×(3/4)n×H

a=2H..........r=3/4

However we have to subtract H because up to the first bounce, the ball only travel H instead of 2H

Therefore the total distance travel up to the Nth bounce is

For N=3 one obtains

D=3.625H