Question

A ball is dropped from 2.00 and rebounds to a height of 1.75m. What is the maximum height it will achieve after bouncing 7 more times?

Answer 1

A ball dropped from height , just before hitting the ground will achieve, a velocity of:

........ EQ1

Now, the ball will rebound with the velocity just after hitting ground,

......EQ2

where is the coefficient of restitution and it lies between 0 and 1 (perfectly elastic collision).

Now, this ball will achieve a height and again will turn towards the ground. This ball will achieve a velocity (just before hitting ground) same as the velocity . So we can write, similar to EQ1:

........ EQ3

Comparing EQ2 and EQ3, we get,

..........EQ4

EQ4 tells us that the successive rebound height will be times of the previous achieved height.

Lets say is the first drop height and is the first rebound and so on.

Using EQ4 we get,

we find e by substituting , we get

......... EQ5

similarly,

.........EQ6

Since we need to find the rebound height after 7 more rebounds, for us . So we solve EQ 6 using value from EQ5