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.
Answers
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ANSWER::
Mass of man , M = 50 kg
Mass of pillow , m = 5 kg
When pillow is pushed by man , the pillow will go down while the man goes up . It becomes the external force on system which is zero.
Acceleration of centre of mass is 0
Velocity of centre of mass is constant
As initial velocity of system is 0
Therefore , M x V = m x v [Equation 1]
Given => Velocity of pillow , v = 80 ft/s
Relative velocity of pillow with respect to man (V₁)
V₁ = v - V = v - (- V) = v + V
v = V₁ - V
Putting it in Equation 1
M x V = m ( V₁ - V)
50 x V = 8 - V
V = 8/11 m/s
Therefore , absolute velocity of pillow , v' = 8 - 8/11 = 8 - 0.727 = 7.2 ft/s
And time taken to reach the floor = S / v' = 8 / 7.2 = 1.11 seconds
Mass of wall is very much higher than pillow
So , velocity of block before collision = Velocity after collision
Time of ascent = 1.11 seconds
Total time taken = 1.11 + 1.11 = 2.22 seconds
Hope it helps!
