Two balls of equal size are dropped from the same height from the roof of a building. the mass of ball a is twice that of ball b, m subscript a equals 2 m subscript b. when the two balls reach the ground, how do their kinetic energies compare?

The mass of ball a is twice the mass of ball b:

This means that the initial potential energy of ball a () is twice the potential energy of ball b ():

When the two balls reach the ground, the potential energy of each ball has converted into kinetic energy (since now their altitude is h=0), because the total mechanical energy of each ball must be  conserved. Therefore:


and so the kinetic energy of ball a must be twice the kinetic energy of ball b: