In a gravity-free hall, an experimenter of mass 50 kg is resting on a 5 kg pillow at a height of 8 ft above the floor. The experimenter pushes the pillow downwards such that it begins falling with a speed of 8 ft/s . The pillow undergoes a perfectly elastic collision with the floor, rebounds, and eventually reaches the experimenter's head. Determine the total time elapsed in this process.

Step-by-step solution

By the principle of conservation of momentum, the initial momentum of the system is zero. When the experimenter pushes the pillow downwards, the experimenter moves upwards. m_ pillow v_ pillow = m_ exp v_ exp 5 8 = 50 v_ exp v_ exp = 0.8 ft/s The time taken by the pillow to reach the floor is: t₁ = 8 ft 8 ft/s = 1 s During this time, the experimenter moves upwards. The height of the experimenter from the floor at t₁ = 1 s is: H_ exp = 8 + v_ exp t₁ = 8 + 0.8 1 = 8.8 ft The pillow undergoes a perfectly elastic colli