Physics

To solve this problem, we need to find the ratio of the kinetic energies of the two balls just before they hit the ground.

 

Use the law of conservation of mechanical energy.

Since there is no air resistance, mechanical energy is conserved. The total mechanical energy (kinetic + potential) at the top will equal the total mechanical energy just before hitting the ground.

 

At the top, the balls have potential energy (PE) and no kinetic energy (KE), since they are at rest. As they fall, the potential energy is converted into kinetic energy. The potential energy at the top is given by:

At the bottom, just before hitting the ground, the potential energy becomes kinetic energy (KE):

 

Calculate the kinetic energy for each ball.

- For the first ball with mass dropped from height :

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