After striking a floor a certain ball rebounds `(4/5)^(t h)` of the height from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of `120` metres.

Explanation

To solve the problem of finding the total distance a ball travels after being dropped from a height of 120 meters and rebounding to \( \frac{4}{5} \) of the height from which it fell, we can follow these steps:

### Step-by-Step Solution:

1. **Initial Drop:**
The ball is dropped from a height of 120 meters. This is the first distance traveled.
\[
\text{Distance}_1 = 120 \text{ meters}
...