the total time taken for a bouncing ball to come to rest if the initial height is h and the coefficient of restitution is e is given by the formula :
T = [ ⟨ 1 + e ⟩ / ⟨ 1 - e ⟩ ] * ⟨ √ ( 2 * h / g ) ⟩
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Initial speed of ball just before it collide with the floor from height h is given by
now after it collide with the floor with rebound height is h/2 is given by
now we have to use the formula of coefficient of restitution
so the coefficient of restitution is 0.707 in this collision
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If there happens to be a little heap of gunpowder lying on the table where the ball hits it, it may bounce back with a faster speed than it had immediately before collision. If the collision is somewhat inelastic it will then rise to a height h1=e2h0 and it will take a time et to reach height h1 .
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