I've attached the question as an image below as it's a graphical question.
It simply states:
"The diagram shows a gas particle about to collide elastically with a wall.
Which diagram shows the correct change in momentum that occurs during the collision?"
The ball, mass m, collides with the vertical wall at an angle θ to the horizontal, at velocity v.
The answer is B, but I can't quite understand why.
I feel as though using sin/cosine in this question is unnecessary, but I understand the ball initially has horizontal component of velocity vcosθ and vertical component vsinθ. The collision is elastic, so I believe the ball will bounce off at a trajectory 90° to its initial trajectory, going essentially "north-east".
However I don't understand why, in answer B, one of the momentum directions is south-east. Though, none of the answers really make sense to me, aside from potentially C.
Any help would be greatly appreciated, thank you.
Best Answer
Change in momentum is equal to $\vec{p}(final) - \vec{p}(inital) $. In (C) final momentum and initial momentum have been added instead of subtracted so it is incorrect. You are also assuming $\theta= 45°$, so the final trajectory will make an angle of $2\theta$ with the inital trajectory (in general) and the "south-east" vector is nothing but $-\vec{p}(inital)$