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. The time elapsed in the process is ______ s.

Options

• 1.22

• 2.22

• 3.22

• 4.22

Answer 1

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. The time elapsed in the process is 2.22 s.

Explanation:

m₁v₁ = m₂v₂

⇒ 50 v₁ = 5 × 8

⇒ v₁ = 0.8 ft/s

Now d_p – 2 × (d_f) = d_M

⇒ v₂t – 2 × 8 = v₁ × t

⇒ t = `16/("v"_2-"v"^1)`

= `16/7.2`s

= 2.22 s