# Particles colliding at greatest height [closed]

It's the very last part. Surely it is wrongly printed because

$$(\sqrt3-1)(\sqrt3+1)=2$$

And coefficient of restitution (e = separation speed / approach speed) should be between 0 and 1.

So, it's easy to calculate that $$v=\sqrt{\frac{2}{3}}u$$

and so we have:

approach speed = $$\sqrt{ga(3-\sqrt{3})}\times(\sqrt{\frac{2}{3}}+1)$$

And at moment of collision momentum is conserved horizontally (particles have same mass and so that cancels) and so:

$$\sqrt{ga(3-\sqrt{3})}\times(1-\sqrt{\frac{2}{3}})=v_2$$

Where $$v_2$$ is particles B's horizontal velocity after the collision = separation speed.

and so we have:

$$e=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\approx0.101$$

Thanks for any help, Mitch.

## closed as off-topic by ACuriousMind♦Feb 11 at 17:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ACuriousMind
If this question can be reworded to fit the rules in the help center, please edit the question.

• Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. – ACuriousMind Feb 11 at 17:01
• I think this should be reopened, as the OP seems to have a legitimate question about a possible error in the question itself. The issue (as I see it) is whether (or not) the coefficient of restitution can legitimately be greater than one. – StephenG Feb 11 at 17:07
• I certainly didn't intend to post off topic\infringe any rules. Indeed I am asking if the question can be correct as stated given that coefficient of restitution should be between 0 and 1. Further, I have shown that I have made the effort to determine the correct answer. This indeed in an attempt to 'prove' the question wrong. If my reasoning is correct then the answer is wrong and also the coefficient of restitution is indeed between 0 and 1. – user3738290 Feb 11 at 17:24
• @StephenG I don't see anything actually being asked, aside from "Could I please ask for advice on the following question?" and maybe "Thanks for any help" but it's a stretch to consider that the actual question. That doesn't qualify as a specific conceptual question. If the post is edited to clearly ask a specific question - such as "can the coefficient of restitution be greater than one?" - then I'll probably agree with you. But in its current state, I don't think the hold is ready to be removed. – David Z Feb 12 at 7:25