Solving Elastic Collision Homework - Exam Prep Question

[bobred]

Homework Statement

This is an exam prep question

Particle A has mass 3m and velocity i + 2j, it collides with particle B mass m velocity -i + j. Collision is elastic. After collision Particle A is observed to be moving along the +ve y-axis. Find the final speeds of the two particles.(two possible cases)

Homework Equations

Being elastic the kinetic energy is the same before the collision and after.
We are given the answers (3/2,\sqrt{41}/2 or 2,\sqrt{5}.

The Attempt at a Solution

Could someone give me a little nudge in the right direction? I can't see where to begin, what is the state of B after the collision?

Thanks

 

[rock.freak667]

Right, so you can form the conservation of kinetic energy equation.

You also need to use conservation of linear momentum. Momentum before = momentum after.

Since you do not know the magnitudes of the final velocities, here is how I put them as

v_A=λj and v_B=αi + βj

 

[bobred]

Thanks for the reply.

I got that far but can't see how to proceed.

 

[ehild]

As rock.freak suggested write up the equations for both the x and y components of the momentum.

ehild