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(A) The initial potential energy of the ball at height $H = 100\, m$ is $PE_i = mgH$.When the ball hits the ground,$20\%$ of its energy is lost,meanin

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$80$

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(A) The initial potential energy of the ball at height $H = 100\, m$ is $PE_i = mgH$.When the ball hits the ground,$20\%$ of its energy is lost,meaning $80\%$ of the energy is retained.The new potential energy at the maximum height $h$ reached after the bounce is $PE_f = mgh$.According to the energy conservation principle,$PE_f = 0.80 	imes PE_i$.Therefore,$mgh = 0.80 	imes mgH$.Canceling $mg$ from both sides,we get $h = 0.80 	imes H$.Substituting $H = 100\, m$,we get $h = 0.80 	imes 100 = 80\, m$.

An inelastic ball is dropped from a height of $100\, m$. Due to the impact,$20\%$ of its energy is lost. To what height will the ball rise?

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