Solving 2D Elastic Collision Problem in Physics

[mgrantbaker]

Came across this one in my freshman physics book:

A particle of mass 1m is traveling along the x-axis at velocity V1. It collides elastically with a second particle of mass 3m traveling at velocity V2. The first particle (1m) moves off at 0.92m/s at 48º to the x-axic. The second particle (3m) moves off at 1.2m/s at 17º to the x-axis. Find two sets of possible values for the initial velocities for both particles and the direction of the second particle (3m).



I've tried brute forcing it with trigonometry/dot-producting the momentum equation and using that with conservation of energy, but I ended up with an equation for the initial direction that was way too complex to solve. Also tried reversing the collision, shifting the angles, and then translating into a rest frame for one of the particles. That approach yielded a direction for the 3m particle that was close to one of the two possible answers, but still not right. Plus, my math (which probably has some mistakes) didn't leave the potential for two results.

I haven't attempted a full vector-based analysis (breaking the collision into normal and trangent vectors) since this is from a freshman level book, and that method is beyond the scope of the chapter. So what am I missing here?

 

[zcd]

If the collision is elastic, then you can use conservation of kinetic energy. Also, since velocities are constant before and after the collision no external forces are acting on the projectiles and momentum is conserved, so you can separate the momentums into equal x and y components.