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First of all ... I think you're talking about either the magnitude of the momentum, or the magnitude

of the velocity, not the magnitude of the objects.

Now ... you're obviously skating around the subject of vectors here, recognizing that both the

velocity and the momentum are vector quantities.

If, as you say, the two objects have " ... the same momentum ... ", then you're saying that their

momentum vectors are equal. If so, then you'd have to say that yes, since the momentum vectors

are equal, the momentum vectors and the velocity vectors must all have the same direction.

But if the two momenta only have equal magnitudes, then they ... and the velocities ... can be in

any two directions, not necessarily related.

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Q: If two objects have the same momentum do their magnitudes necessarily have the same directions?
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