A ball is thrown from a height of 200m. Once the ball strikes the floor it bounces back to half the original distance. At another strike to the floor it again bounces back to half the previous height and this goes on till it stops. Approximately how much total distance the ball has travelled before it stops. (Assume that the ball is bouncing at the same point and there is no horizontal distance covered by the ball)
200m
400m
600m
None of the Above
Cannot be determined
Answer :600 m
Solution (Fast Approach)
When the ball falls from 200 m. It bounces back to 1/2*200 = 100 m. Then it comes back to ground covering 100 m, which he had bounced, covering a total of 2*100 m
Now it bounces back to 1/2*100 = 50 m and so on
Total Distance covered by the ball = Initial 200 m + 2 * (100 + 1/2 * 100 + 1/2 * 1/2 * 100 + 1/2 * 1/2 * 1/2 * 100 ------- infinite)
Note: This is an infinite G.P. series. Sum of G.P Series is a/1-r where "a" is the starting term and "r" is common ratio. In the above equation a = 100 and r = 1/2
=> 200 + 2*[100/(1-1/2)] = 200 + 400
=> 600 m
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