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Question

Consider a gravity- free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process.

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Solution

By momentum conversation,
Mu=mv
50u=50×8
u=0.8ft/sec
Time taken t1 to reach pillow at floor
t1=88=1sec.
In time t1 man move up height h1
h1=u×t1=0.8×1=0.8ft.
At time of rebound pillow distance between head of experimenter's and floor or pillow,
H=(8+0.8)=8.8ft.
TIme taken to cover 8.8ft distance relative to experimenter.
Relative velocity after rebound=vu=80.8=7.2ft.
Time taken t2=8.87.2=1.222sec
Total time elapse=t1+t2=1+1.22=2.222sec.

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