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, AccidentalFourierTransform Mar 31 '17 at 18:51

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  • $\begingroup$ 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 $\endgroup$ – ZeroTheHero Mar 31 '17 at 12:43
  • $\begingroup$ 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 $\endgroup$ – 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.


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