Conservation of Momentum question

[David112234]

Homework Statement

Two carts sit on a horizontal, frictionless track; the spring between them is compressed. The small cart has mass m, and the mass of the larger cart is M = 4.65m.
NOTE: Every velocity needs magnitude and direction (given by the sign).

a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity v = +8.71 m/s.
- Find the velocity of the larger cart. V = (answer) m/s
- Assume now that the mass of the smaller cart is m = 6.36 kg. Assuming there is no loss of energy: find the energy stored in the spring before the explosion. Wk = (answer)J
- If the spring has spring constant k = 276 N/m: find x, the distance the spring was compressed before the "explosion".

Homework Equations

F=kx
PE(spring) = 1/2 kx^2
MV+MV=MV+MV

3. The Attempt at a Solution
part a) I know that if both carts have the same mass then both will be moving away from each other at the same speed after the spring explodes, so it would be -8.71 . But one cart has higher mass, so one cart will move faster away. So I use the conservation of momentum formula
MV+4.65M*O = M8.71+4.65M*V
what do I do, solve for V? I cant, the algebra does not work out, am I missing a formula?

 

[haruspex]

MV+4.65M*O = M8.71+4.65M*V
what do I do, solve for V? I cant, the algebra does not work out, am I missing a formula?

Why do you have a V on the left?
Note that every term has a factor m. What does that allow you to do?