A child drops a rubber toy from a height of 2 meters. Each time it hits the floor; it rebounds to three-fourths of the height from which it fell. The toy stops bouncing if the height of the next bounce would be less than 60 cm. How many times will the toy strike the ground before coming to rest?

(a) 4 times

(b) 6 times

(c) 5 times

(d) 7 times

Question

A child drops a rubber toy from a height of 2 meters. Each time it hits the floor; it rebounds to three-fourths of the height from which it fell. The toy stops bouncing if the height of the next bounce would be less than 60 cm. How many times will the toy strike the ground before coming to rest?

(a) 4 times

(b) 6 times

(c) 5 times

(d) 7 times

ONLiNE UPSC · Accepted Answer

Initial height = 200 cm
Rebounds to &frac34; each time:
1st hit &rarr; 200 &rarr; bounce to 150
2nd hit &rarr; 150 &rarr; bounce to 112.5
3rd hit &rarr; 112.5 &rarr; bounce to 84.375
4th hit &rarr; 84.375 &rarr; bounce to 63.28
5th hit &rarr; 63.28 &rarr; bounce to 47.46 &rarr; less than 60 &rarr; stop

Hence, correct option is c.

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