GATE ME 2018 Set 1 — Question 38
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Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
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Question
A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, . It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of
Correct answer
(C) 4
Solution
The initial velocity is m/s. The time taken to reach the ground for the first time is s.
The impact velocity is m/s. After the first collision, the velocity becomes m/s.
The time for the first bounce cycle is s.
The time for subsequent bounces forms a geometric progression with common ratio .
The total time is:
s.
The impact velocity is m/s. After the first collision, the velocity becomes m/s.
The time for the first bounce cycle is s.
The time for subsequent bounces forms a geometric progression with common ratio .
The total time is:
s.
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