Colliding particles with equal masses with given elasticity

[Superfluous]

If the two particles with equal masses m collide with elasticity E = 0.650 , what are the final velocities of the particles? Assume that particle 1 has initial velocity v and particle 2 is initially at rest.

Give the velocity $$v_{1}$$ of particle 1 and the velocity $$v_{2}$$ of particle 2. Express the velocities in terms of v.

What I know...

$$mv_{1i}+mv_{2i}=mv$$

$$v_{2f}-v_{1f}=Ev}$$

I tried to use these two equations to solve for it, but it doesn't work out. My problem is that I know I'm supposed to use these equations to solve this, but I can't figure out exactly what to do with them. Solving the first equation for v and then substituting it into the second equation doesn't get me anywhere.

 

[Mindscrape]

By elasticity do you mean coefficient of restitution? If so it is

$$\epsilon = \frac{|v_{2f} - v_{1f}|}{|v_{2i}-v_{1i}|}$$

you might have the wrong formula.

Also, another problem I see is that you are assuming an inelastic collision with your momentum equation. This is not necessarily true. Inelasticity works when your coefficient of restitution is zero, or approximately low.

 

[saket]

What I know...

$$mv_{1i}+mv_{2i}=mv$$

I guess, the correct formula is, $$mv_{1f}+mv_{2f}=mv$$.
Now solve, you should get.