Consider a gravity-free hall in which a experimenter of mass $50 \mathrm{~kg}$ is resting on a $5 \mathrm{~kg}$ pillow, $8 \mathrm{ft}$ above the floor of the hall. He pushes the pillow down so that it starts falling at the speed of $8 \mathrm{fts} / \mathrm{s}$. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process.
$V_{p m}=8$
(velocity of pillow w.r.t man)
$V_{p m}=\overline{V_{p}}-\overline{V_{m}}=V_{p}+V_{m} \quad$ as $\left\{\overrightarrow{V_{m}}=-V_{m}\right\}$
Use C.O.L.M,
$M_{m} V_{m}=M_{p} V_{p}$
$50 V_{m}=5 \times\left(V_{p m}-V_{m}\right) V_{p m}=8$
$V_{m}=\frac{8}{11}$
$V_{p}=V_{p m}-V_{m}$
$\begin{aligned} V_{m} &=\frac{8}{11} \\ V_{p} &=V_{p m}-V_{m} \end{aligned}$
Time taken for going down= $\frac{x}{V_{p}}=\frac{8 f t \times 11}{80 f t / s}$ $t=\frac{11}{10}=1.1$ $\mathrm{sec}$
$t=\frac{11}{10}=1.1 \mathrm{sec}$
Total time taken (up+ down) $=2 t=2(1.1)=2.2 \mathrm{sec}$
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