Question
A ball is dropped from a height of 120 metres. After each
bounce, it rises to one-fourth of the height from which it fell. What is the total distance the ball travels before coming to rest?Solution
Distance travelled in 1 st  fall = 120 m
Height to which the ball will rebound in 1 st  fall = 120/4 = 30 metres
Height to which the ball rebounds in 2 nd  fall = 30/4 = 7.5 metres
Therefore, distance travelled by ball = 120 + 30 + 30 + 7.5 + 7.5……. upto infinity
= 120 + 2 × (30 + 7.5 + up to infinity)
= 120 + 2 × 30/{1 – (1/4)} [sum of infinite G.P. = a/(1 – r)]
= 120 + 60 × 4/3 = 120 + 80 = 200 metres
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