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.

• A. 2.88 s
• B. 1.22 s
• C. 2.22 s
• D. 0.22 s

Answer 1

The correct option is C

2.22 s

The situation shown is depicted in following figure.

Let the velocity of man be v(wrt ground) upwards. As the momentum is conserved,

$5\times 8=50\times v$

$v=0.8ft/s$

Pillow takes 1s to reach the wall.

As the collision of pillow with the wall is elastic, pillow comes back towards $P$ with $8ft/s$.

Now it again takes 1s to reach $P$ from the wall.

Total time consumed = 2s

But in these 2s the man would have moved $(2\times 0.8)$ ft upwards.

Let time taken by pillow to reach the man from $A$ be $t$.

So $v$ distance covered by man = $0.8t$ further.

And distance that pillow has to cover = $(1.6+0.8t)$

As the pillow is hitting the man, both should have covered the same distance

Therefore, $8t=1.6+0.8t\Rightarrow t=0.22s$

$\therefore$ Total time consumed = $2+0.22=2.22s$