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A body dropped freely from a height 'h' on to a horizontal plane, bounces up and down and finally comes to rest. The coefficient of restitution is 'e'. The

ratio of velocities at the beginning and after two rebounds is?



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Coefficient of restitution for an elastic/inelastic collision = e =
               Relative velocity after collision / relative velocity before collision

Let us say the body has a velocity of V just before collision with the plane.

velocity of the body after rebounding is  V1 =  e * V  directed upwards.

Velocity of the body just before rebounding a second time = V1 = eV directed downwards.

Velocity of the body just after rebounding second time = e V1 = e² V

Ratio = V : 2² V  = 1 : e²

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