Two cars have masses and , where . They are traveling in the...

Question

Two cars have masses and , where . They are traveling in the same horizontal direction with equal kinetic energies. What is the relationship between their momenta, and ?

Given that two cars have masses and , where , and they are traveling in the same horizontal direction with equal kinetic energies, we are asked to compare their momenta and .

Kinetic Energy Formula

The kinetic energy of an object is given by:

where:

is the mass of the object

is the velocity of the object

Since both cars have equal kinetic energies, we have:

Substituting the formula for kinetic energy for each car:

Solving for Velocities

We can express the velocities of the cars in terms of their masses:

Since , this implies that .

Momentum Formula

The momentum

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