An object falls from a height of $20 \mathrm{~m}$ above the ground. After striking the ground, it lo

Question

An object falls from a height of $20 \mathrm{~m}$ above the ground. After striking the ground, it loses $40\%$ of its kinetic energy. The height up to which the object can rebound from the ground is

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(d) : The initial potential energy at height $h = 20 \mathrm{~m}$ is $U_i = mg(20) = 20mg$. By conservation of energy, the kinetic energy just before striking the ground is $K_i = 20mg$. Since it loses $40\%$ of this energy upon impact, it retains $60\%$ of its kinetic energy. The kinetic energy after impact is $K_f = 0.60 	imes 20mg = 12mg$. This remaining kinetic energy is converted back into potential energy as it rebounds to height $h'$. Thus, $mgh' = 12mg$, giving $h' = 12 \mathrm{~m}$.