Two cannonballs a and b are fired from the ground


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Two cannonballs are dropped from a second-floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first-floor window at height above the ground, the relation between their kinetic energies, KA and KB, is

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The relation between the kinetic energies of the freely falling balls A and B is obtained as \frac{KE_{A}}{KE_{B}} =\frac{1}{4}.

Kinetic Energy

The kinetic energy of an object depends on the mass and velocity with which it moves.

While under free-fall, the mass of an object does not affect the velocity with which it falls.

So, the velocities of both the balls are the same.

Let the mass of ball A is 'm'

So, the mass of ball B is '4m'

The kinetic energy of ball A is given by;

KE_{A}=\frac{1}{2} mv^2

The kinetic energy of ball B is given by;

KE_{B}=\frac{1}{2} 4mv^2 = 2mv^2

Therefore, the ratio of kinetic energies of A and B is,

\frac{KE_{A}}{KE_{B}} =\frac{1}{4}

Learn more about kinetic energy here:

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