A tennis ball is released from a height of 2.0 m above the floor, and then bounces three times. With each bounce, dissipative forces cause it to lose 16.0% of its mechanical energy. How high does it reach after the third bounce?

12 cm

120 cm

140 cm

120 mm

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aristocles aristocles · Answer 1 · 2019-01-29T01:12:31+01:00

Here initial total potential energy of the ball is given by

[tex]U = mgh[/tex]

now on each bounce it will lose 16% of the energy

so at each bounce it will have 84% of initial energy

so here we will have total energy after first collision

[tex]U_1 = 0.84(mgh)[/tex]

After 2nd collision total energy is given as

[tex]U_2 = 0.84(0.84mgh)[/tex]

now after third collision the final energy is given by

[tex]U_3 = 0.84(0.84)(0.84mgh)[/tex]

so the final height is given as

[tex]H = 0.84(0.84)(0.84)h[/tex]

[tex]H = 0.593(2) = 1.185 m[/tex]

so after third bounce its height will be 1.185 m