Consider a gravity- free hall in which an experimenter of mass $50 k g$ is resting on a $5 k g$ pillow, $8 f t$ above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of $8 f t / s$ . 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,
$M u = m v$
$50 u = 50 \times 8$
$u = 0.8$ ft/sec
Time taken $t_{1}$ to reach pillow at floor
$t_{1} = \frac{8}{8} = 1$ sec.
In time $t_{1}$ man move up height $h_{1}$
$h_{1} = u \times t_{1} = 0.8 \times 1 = 0.8$ ft.
At time of rebound pillow distance between head of experimenter's and floor or pillow,
$H = (8 + 0.8) = 8.8$ ft.
TIme taken to cover $8.8$ ft distance relative to experimenter.
Relative velocity after rebound= $v - u = 8 - 0.8 = 7.2$ ft.
Time taken $t_{2} = \frac{8.8}{7.2} = 1.222$ sec
Total time elapse= $t_{1} + t_{2} = 1 + 1.22 = 2.222$ sec.

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