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

Kinetic energy is a scalar quantity and momentum is a vector quantity. Therefore, kinetic energy will remain unchanged even when the velocity changes direction if its magnitude remains same. But momentum will not remain same if direction of velocity is changed even if magnitude remains unchanged.

In the given problem, magnitude of velocity remains unchanged but its direction has changed so its momentum will also change. A force must be acting on the car.