Question

A rubber ball is dropped from a height of 4 meters onto a concrete floor. It bounces to $75\%$ of its original height and drops back down, bouncing many times in ever-smaller bounces. If it did this forever how much total distance did the ball cover?

• A. 30m
• B. 26m
• C. 28m
• D. 24m

Answer 1

The correct option is C

28m

Distance travelled before first hit = 4 meters.
Distance travelled before second hit = 4+0.75 $\times$4$\times$2
Distance travelled before third hit =$4+0.75\times 4\times 2+(0.75{)}^2\times 4\times 2.$ And so on.
Hence required distance
$=4+8\times 0.75+8\times {0.75}^2+8\times {0.75}^3+............=4+8\times \frac{0.75}{0.25}=28m$