This situation is possible due to the relationship between kinetic energy, mass, and velocity. Kinetic energy (\( KE \)) is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
Since the two objects have equal masses, the only factor that can cause one object to have greater kinetic energy than the other is their velocities. Specifically, if one object is moving at a higher velocity than the other, it will have a greater kinetic energy—even though both objects have the same mass.
For example, consider the following:
- Object A has a mass of \( m \) and a velocity of \( v_1 \).
- Object B also has a mass of \( m \), but its velocity is \( v_2 \) where \( v_2 > v_1 \).
In this case, the kinetic energies would be:
\[ KE_A = \frac{1}{2} m v_1^2 \] \[ KE_B = \frac{1}{2} m v_2^2 \]
If \( v_2 \) is significantly greater than \( v_1 \), then \( KE_B \) will be greater than \( KE_A \), illustrating how it is possible for one object to have greater kinetic energy than the other even when their masses are the same.