Question

A rubber ball of mass m is dropped from a height h. If the ball loses energy on each bounce so that its speed just after each bounce is 90% of its speed just before each bounce, then Önd an expression for the height the ball reaches after the 3rd bounce

Answer #1

speed after bounce is 0.9Vo

Kinetic energy before any bounce = Ko

Kinetic energy after bounce = (0.9)^{2} Ko = 0.81 Ko

kinetic energy before first bounce = mgh (initial potential energy
of ball is converted to kinetic energy just before bounce)

Kinetic energy after 3rd bounce = (0.81)^{3} mgh

= 0.53 mgh

Height after 3rd bounce = 0.53h

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