- #1

ph123

- 41

- 0

Express answer in terms of the initial velocity, v.

My conservation of energy equation for the two particles is (I already canceled out the masses):

v1^1 + 0.5v2^2 = v^2

My conservation of momentum equation is (masses already cancelled):

2v1 + v2 = 2v

Thus,

v2 = 2v-2v1

v1 = (2v-v2)/2

I tried plugging these values for v1 and v2 into the conservation of energy formula to try and isolate v for each variable. For v1, I ran into difficulty because of the middle term of the binomial equation, -8vv1.

v1^1 + 0.5v2^2 = v^2

v1^2 + 0.5[(2v-2v1)(2v-2v1)] = v^2

v1^2 + 0.5[4v^2 - 8vv1 + 4v1^2] = v^2

-v^2 = v1^2 - 4vv1 + 2v1^2

3v1^2 - 4vv1 = -v^2

From here I spent like 10 lines trying to rearrange terms to separate v from that middle term (now -4vv1), but am unable to do so. Any ideas? Thanks!