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