Solving Collision Problem: Finding Speeds of Balls After Impact

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A ball moving at 15 m/s collides with an identical stationary ball, resulting in the first ball deviating at -41° and the second at 24°. The discussion involves setting up equations for conservation of momentum in both x and y components. The equations are correctly established, allowing for the determination of the final speeds of both balls. By solving one equation for a variable and substituting it into the other, the speeds can be calculated effectively. The approach emphasizes using vector components to find the final velocities after the collision.
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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?
 
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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.
 
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).
 
Well if you solve for each then you can add their squares and find the square root to find the magnitude of the vector!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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