GATE 2018 ME (ME1) – Question 38
A point mass is launched vertically upwards at 4 m/s from ground at t = 0. After each ground impact it loses 20% of its impact speed. With g = 10 m/s² and negligible air drag, total time until it stops bouncing is ______.
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Correct answer: (C) 4 s
Explanation
The first up-and-down flight lasts $2(4)/10=0.8$ s. Each subsequent flight is 0.8 times the preceding one. Sum the geometric series: $T=0.8/(1-0.8)=4$ s (C). Infinitely many diminishing bounces accumulate at this finite limiting time in the ideal model.