Physics

Given that two objects have equal momenta, with masses and , where , we need to compare their kinetic energies.

Momentum and Kinetic Energy Formulas

The momentum of an object is given by:

where is the mass and is the velocity of the object.

The kinetic energy of an object is given by:

Expressing Velocity in Terms of Momentum

Since both objects have equal momenta, we can write:

For the two objects, the momenta are:

Since , we have:

Solving for and :

Kinetic Energy Comparison

Now we can substitute into the kinetic energy formula for each object.

For object 1: