# Change in momentum for gas particle collision with wall

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.

• Please use homework-exercises tag for such questions in future. – Abhay Hegde May 13 '19 at 13:48

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 $$-\vec{p}(inital)$$