Momentum and direction?

Question

Ok, so I got some answers on my previous question, but I'm still confused.
The complete question I have to answer is as follows:
- Which has greater momentum, a 1 ton care moving at 50km/hr or a 2 ton truck at 25km/hr?
- If the car and truck move in opposite directions what is the car's momentum in regards to the truck and vice versa. Why does the momentum differ from the first case?

I know that momentum = m*v, so I can figure out the first part of the question, but why is my professor stating in his last sentence that the momentum will differ if they're going in opposite directions?

I'm confused....Please help.... ;-)

Answer 1

Good.

Apparently the book was not the problem.
Momentum is
a) vector
b) non-invariant
c) co-variant wrt Galilean transformations.

Mass is invariant scalar, it remains the same in all frames of references.
Momentum is co-variant vector, it changes when you switch to another frame of refence according to the formula
P_new = P_old - MV_(new_frame_wrt_old_frame)

For this reason the statment "momentums are the same" can be true only in one particularar frame of reference.

Answer 2

The value, or magnitude, of the momentum is the same for the car and the truck. However, momentum is a vector. If the car is going due East, and the truck is going due West, for example, they have different momentums, even though their magnitudes are the same. You must specify both magnitude and direction to get the momentum vector. Your professor is trying to make you aware that you must specify both magnitude and direction for momentum. It is not sufficient to only specify the magnitudes.

Answer 3

Momentum is a vector quantity. It has an amount and a direction.
The amount of momentum, either 1 times 50 or 2 times 25 will be equal.
If the direction is different, the momentum is different.

Answer 4

Relative velocity is different than that with respect to grownd.

From the car window, it looks like the truck is moving away at the velocity V = Vcar + Vtruck. This is a different velocity. Thus momentum will be different.