I'm having some trouble with a homework exercise and I'd really appreciate some help! I've done the first part correctly (according to the solution sheet), but I can't seem to get the second part right.
**The first part of the problem:
Two particles collide elastically. If m1 = 2 kg and m2 = 1 kg and the initial velocities of the two particles are u1 = (3i + 4j) ms-1 and u2 = (7i + j) ms-1 respectively, find (i) the velocity of the centre of mass and (ii) the momentum of each particle in the centre-of-mass frame.**
Okay, so far I have:
i) V(CM) = (13/3i + 3j)ms-1 & (ii) p'(1,2) = +/-(8/3i - 2j)kgms-1
**The second part of the problem:
After the elastic collision, the particles separate so that particle 1, as viewed from particle 2, moves away along the positive x-axis (i.e. in the direction of the unit vector i). Find the final velocity of each particle in the laboratory frame.**
This is where I'm getting confused.
To find the final velocities v1 and v2 (and knowing that the collision is elastic so V(rel) = -U(rel)), I used the equations:
v'1 = (m2/M)*V(rel) -----> v1 = v'1 + V(CM) & v'2 = -(m1/M)*V(rel) -----> v2 = v'2 + V(CM)
Which gives me the values:
v1 = (4/3i - j)ms-1 & v2 = (17/3i + 2j)ms-1
Which, according to the solution sheet are incorrect. The correct values are in fact:
v1 = (6i + 3j)ms-1 & v2 = (i + 3j)ms-1
Now I know I'm obviously missing something here, but I'm not sure what. Could somebody please explain this to me? Is it something to do with the information given on how particle 1 moves away along the positive x-axis relative to particle 2?
I've spent a while trying to solve this so any help would be greatly appreciated (sorry for long post)!