Question 111

A tennis ball is initially dropped from a height of 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen. The total distance that the ball travels before it comes to rest is

Solution

While going down the ball will first cover $$180$$m, then $$\frac{180*3}{5}$$, then $$\frac{180*3*3}{5*5}$$ and so on.
After rebouncing the ball will cover $$\frac{180*3}{5}$$, then $$\frac{180*3*3}{5*5}$$ and so on
Thus, there are 2 infinite G.Ps here one of $$180$$, $$\frac{180*3}{5}$$, $$\frac{180*3*3}{5*5}$$,......
and other $$\frac{180*3}{5}$$, $$\frac{180*3*3}{5*5}$$,.........
Total distance covered by the ball = Distance covered while going up + Distance covered while going down
= $$\frac{180}{1-\frac{3}{5}} + \frac{180*\frac{3}{5}}{1-\frac{3}{5}}$$ = $$720$$ m.
Hence, option C is the correct answer.

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