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 hail. 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.
Mass of the man is M = 50 kg,
Mass of the pillow is m= 5 kg,
Experiment height 8 ft above the floor of the hail.
He pushes the pillow down so that it starts falling at a speed (V) of 8 ft/s.
When the pillow is pushed by the man the pillow will go down with velocity v while the man will go up with velocity v’. It becomes the external force on the system is zero.
Acceleration of centre of mass is zero,
Velocity of centre of mass is constant.
Now, as the initial velocity of the system is zero
_______ (1)
Relative velocity (V) of pillow with respect to man will be
Putting the value in equation (1)
Therefore, absolute velocity of the pillow = 8 – 0.727 = 7.2 ft/s
Time taken to reach the floor will be
As the mass of the man is much greater than mass of pillow
By conservation of momentum
Velocity before collision = velocity after collision
Therefore, time of ascent = 1.11 s
Thus, total time taken = 1.11 + 1.11 = 2.22 s