Physics

We are given that the mass ratio of two objects is and their kinetic energy ratio is . We need to find the ratio of their momenta.

 

Recall the formula for kinetic energy and momentum

The kinetic energy of an object is given by:

The momentum of an object is given by:

 

Express kinetic energy and momentum

We know the kinetic energy ratio:

Substitute the formula for kinetic energy into this ratio:

 

Solve for the velocity ratio

We are also given that the mass ratio is

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