Inelastic collision between two perpendicular particles

[physics148]

Homework Statement

A particle of mass m1 collides with a particle of mass m2 initially moving at right angles to it(see Figure 1 below). Calculate the final velocities of each particle, and the angles at which the particles leave the collision site( as measured with respect to the original direction of m1) assuming that the coefficient of restitution is e=0.4, m1=3kg, m2=2kg, and the initial speeds of the particles are v1=2m/s, and v2=3m/s respectively.

Homework Equations

conservation of momentum
coefficient of restitution, e = |Vsep|/|Vapp|

The Attempt at a Solution

I attempted to solve this question using the conservation of momentum, as well as the coefficient of restitution equation. My work is shown in the figure below. Where I get confused now, is that I think I have 3 unknowns (v1', theta1 and theta2) in 2 equations. I thought about using energy conservation to obtain more equations, but then since this collision is inelastic, wouldn't I have to know the Q term(the energy lost) in order to use them? Any help would be greatly appreciated.

 

[TSny]

I don't think this question is well-defined if the usual definition of coefficient of restitution is applied.

See http://www.brown.edu/Departments/Engineering/Courses/En4/notes_old/oblique/oblique.html

Note how the coefficient of restitution is defined in terms of the normal components of the velocities. But, you don't know the normal direction for this problem.

For example, the answer would be different for the two cases shown below:

These are only two possibilities out of an infinite number. For the possibility shown on the left, the normal direction is the horizontal direction. For the figure on the right, the normal direction is the vertical direction.