How to Balance Masses for Simultaneous Impact in a Momentum Problem?

[delecticious]

Homework Statement

The drawing below shows two laboratory carts (each has a mass of 1.0 kg) X and Y in contact with a compressed exploder spring between them. The mass on cart Y is 2.17 kg, distance A is 60 cm, distance B is 90 cm. What mass must be placed on cart X, such that after the explosion both carts will hit the ends of the track at the same time?

After the explosion has taken place, which of the following statements regarding the kinetic energies, EK, and the magnitudes of the momenta, pi, are correct or incorrect? (Note: The subscripts x and y refer to the carts, not the direction along x or y.)
px < py
Ey = 2/3 Ex
Ex < Ey
py = px/2
px = py

Homework Equations

p = mv

F(delta t)= mvf - mv0

The Attempt at a Solution

What I wanted to do was find the momentum for each of these and then somehow find the time it would take the carts as they are to get to their respective ends, but with no velocities given I'm at a total loss. How should approach this problem? As for the second half, I pretty much suck at true/false type stuff I already guessed at incorrectly 3 times so I'd rather save my remaining 4 guesses. Anyone willing to help me out?

 

[learningphysics]

First deal with the kinematics part. After the explosion suppose X has a velocity vx, and Y has a velocity vy.

What is the relationship between vx and vy? no momentum or forces here... just speed , distance time etc...

 

[delecticious]

I still don't quite get it even with said vx and vy that's only 2 variables and to solve a kinematics problem you need at least 3 known variables.

 

[delecticious]

still looking for help on this one if anyone's willing.

 

[learningphysics]

I still don't quite get it even with said vx and vy that's only 2 variables and to solve a kinematics problem you need at least 3 known variables.

Write an equation relating vx and vy... don't try to solve them... just write the equation... here's the part of the question you need: "carts will hit the ends of the track at the same time"