2D Conservation of Momentum Question

[Techcom0]

A steel ball of mass moving with a velocity of 2.0 m/s [E], strikes a 1.2 kg copper ball initially moving 1.0m/s [W]. The collision is a glancing one, causing the steel ball to have a velocity of 1.5 m/s [W 30 degrees N] and the copper to move in the direction [E 47 degrees S]. Is the collision elastic?

There seems to be so many unknowns in this question, which is why I seemingly can't combine any formulas. How should I attempt to solve this?

 

[Simon Bridge]

To do conservation questions, there is a discipline to keep track of what you know and what you don't.

Start out with "before" - and draw a diagram for the situation.
Drawing diagrams is very good even if the final answer does not require them - they are a computational tool.

Label the diagram with what you know - like the masses and the speeds.
Break any vectors into components - in this case you have E and N components (think of N as the y-axis if it helps).
Any values you don't know, just leave as letters. For eg, you don't know the mass of the east-bound mass - just leave it as m and move on.
What to do about it will become clear later.

Next to the diagram, write out the total momentum in the picture, as two components, and write out the total energy (it's just a magnitude).

Next start a new diagram called "after"
do the same thing - diagram, components, final momentum (vector) and energy.

next you write:
energy: before=after ... check this by doing the math.
momentum: before = after ... check again

of course this is the situation if there are no losses - in which case these are 3 simultanious equations and two unknowns.
if there are losses, there will be no solution that satisfies all three equations.

Does it pan out? Is there a simultanious solution?