Question

Q. A ball is dropped from a height of 81m. Each time it hits the ground, it bounces back up to two thirds of the distance it fell down. Find the total distance covered by the ball when it reaches the top position after the third bounce.

• A. 275
• B. 285
• C. 300
• D. 265
• E. None of these

Answer 1

The correct option is B 285

Initial drop = a = 81
Distance travelled each time after a bounce =$\frac{2}{3}$ of a, r = $\frac{2}{3}$
Distance travelled by ball when it reaches top position of third bounce
$=81+(2\times \frac{2}{3}\times 81)+(2\times (\frac{2}{3}{)}^2\times 81)+(81\times \left(\frac{2}{3}{)}^3\right)=81+108+72+24=285$