Solving Collision Problem: Finding Speeds of Balls After Impact

[lmf22]

A ball moving with a speed of 15 m/s strikes an identical ball that is initially at rest. After the collision, the incoming ball has been deviated by deta1 = -41° from its original direction, and the struck ball moves off at deta2 = 24° from the original direction. What are the speeds of the two balls after the collision?

I set up these two equations:
initial momentum = final momentum

x component: v1(initial) = v1(final)*cos(-41) + v2(final)*cos(24)

y component: 0 = v1(final)*sin(-41) + v2(final)*cos(24)

Did I set up this right?
How would I solve these equations?

 

[Tide]

You have two equations and two unknowns and the relationships are linear! It's easy to solve. For example, solve the 2nd equation for v1_final in terms of v2_final then substitute that result into the first equation which you can readily solve for v2_final -which, in turn, let's you explicitly determine v1_final.

 

[lmf22]

These 2 equations are separate components (X and Y). I can just solve for the 2nd one and plug into the first? I thought I have to solve each one individually and then combine them to find the hypontenuse (V_final).

 

[Tide]

Well if you solve for each then you can add their squares and find the square root to find the magnitude of the vector!