# Finding Speeds of two bodies after elastic collision [closed]

This is a past paper question from FM Mechanics. It's been an hour and I cannot figure out a solution to this question:

Particles of masses m1 and m2 lie at rest on a smooth horizontal plane. Each particle is given a horizontal impulse of magnitude I towards the other particle so that the particles collide directly. Given that the collision is perfectly elastic, find the speeds of the particles after the collision.

Spoilers ahead! - The velocity (answer) of each particle is given in terms of the respective mass of the particle.

## closed as off-topic by garyp, ZeroTheHero, Yashas, Jon Custer, AccidentalFourierTransformMar 31 '17 at 18:51

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" – garyp, ZeroTheHero, Yashas, Jon Custer, AccidentalFourierTransform
If this question can be reworded to fit the rules in the help center, please edit the question.

• Hello and welcome to the Physics SE! Please note that we don't answer homework or worked example type questions. Please see this Meta post and this Meta post – ZeroTheHero Mar 31 '17 at 12:43
• a hint: $v_1 = I/m_1$, $v_2 = I/m_2$. So you know initial velocities and and initial masses. My suggestion would be to take a frame where one is at rest and apply conservation of energy and momentum. Then it is just a matter of finding the nicest method of solution for variables. Also, homework questions are not suitable for this website – lucky-guess Mar 31 '17 at 12:44

I am not going to solve it for you, but I will give you the following hints. As you know the masses you can calculate the respective velocities $v = \frac{I}{m}$. However there are two velocities afterwards and you only know that momentum is conserved: $$I_1 + I_2 = I_3 + I_4 .$$ Well of course you also know that kinetic energy is conserved as the collision is inelastic: $$\sum E_{kin} = const.$$ So know you have two equations and two unknowns. You should be able to derive the velocity equations now.