Q. A rubber ball dropped from a height of 1 m bounces(after hitting the floor) several times,losing 10% of its kinetic energy in each bounce. After how many bounces will the ball not rise above 10 cm?

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A rubber ball dropped from a height of 1 m bounces (after hitting the floor) several times, losing 10% of its kinetic energy in each bounce. The number of times the ball bounces after which it will not rise above 10 cm has to be determined.

Let the mass of the ball be m. At height 1 m, the potential energy of the ball is m*g*1. When it reaches the ground all this energy is converted to kinetic energy and is equivalent to (1/2)*m*v^2. There is a loss of 10% of kinetic energy on each bounce. After the first bounce, the height of reached by the ball is 1*0.9. After the second bounce it is 1*0.9^2. If the ball rises to a height less than 10 cm after N bounces

1*(0.9)^N < 0.1

=> N = 22

The ball rises to a height less than 10 cm after 22 bounces.

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