Physics

We are given two objects with equal masses, and the ratio of their momentum magnitudes is 1:5. We are asked to find the ratio of their kinetic energies.

 

The momentum of an object is given by the formula:

 

Where:

is the mass of the object

is the velocity of the object

 

The kinetic energy of an object is given by the formula:

 

Momentum and Velocity Relationship

Let the momentum of the first object be and the second object be . The ratio of their momentum magnitudes is given as:

 

Since , we can express the ratio of their velocities:

 

Given that the masses are equal (), this simplifies to:

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