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Question

# A ball is dropped from a height of 45 m from the ground. The coefficient of restitution between the ball and the ground is 2/3. What is the distance travelled by the ball in 4th second of its motion. Assume negligible time is spent in rebounding :Take g=10ms2

A
5 m
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B
20 m
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C
15 m
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D
10 m
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Solution

## The correct option is C 15 mLet time taken by the ball to reach the ground be t′ sec.∴ Using s=ut+12g(t′)245=0+12×10(t′)2 ⟹t′=3 secVelocity of ball just before reaching the ground u=√2ghu=√2×10×45=30 m/sVelocity of ball just after collision v=eu=23×30=20 m/sDistance travelled in 4th second i.e t=1 sec, s′=vt−12gt2s′=20×1−12×10×12=15 m

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