Question

1. A car has the same kinetic energy when it is traveling south at 30 m/s
as when it is traveling northwest at 30 m/s. Is the momentum of the
car the same in both cases? Explain

Answer 1

No, the momentum is not the same. The kinetic energy is a scalar quantity, it depends only on velocity magnitude, not the velocity direction. The momentum, however, is the vector quantity. It depends both on velocity magnitude and direction:

$$\mathbf{p} = m\mathbf{v}$$

where $m$ is the mass of the object, $\mathbf{v}$ is its velocity. Bold letters denote vectors.

Thus, in case when velocity points south differs from the case velocity points northwest.

Answer. No, the momentum is not the same.