Two dimensional Elastic Collision

[CalebB-M]

Homework Statement

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The problem statement is: A helium atom traveling at a speed of 240 m/s hits an oxygen atom at rest. If the helium atom rebounds elastically, from the oxygen atom at an angle of 90° with respect to the original direction of motion, what are the final velocities of both atoms. (hint the oxygen is approximately 4 times as massive as the helium.)

Homework Equations

I understand that Momentum is conserved Pi = Pf thus m*v1i + m*v2i = m*v1f + m*v2f
Energy is also conserved in an elastic collision.
1/2m * v^2 = ke

The Attempt at a Solution

I can setup the coordinate system with +x being the initial direction of the helium particle. I also tried writing it in vector notation. my initial setup looked like this
M*[ 240x, 0y, 0z] + 0 (because it is at rest) = M*[0x,sin90*|v1f|y, 0z] + 4M*[cos♤*|v2f|x,sin♤*|v2f|y, 0z]
With ♤ being the unknown direction.
I also attempted to find the magnitude of the velocities by CE, I found that 1/2 M *(240)^2 = 1/2M*(v1f)^2 + 2M*(v2f)^2. Canceling out the mass I found that 240^2 = v1f^2 /2 + 2*v2f^2. I am lost on the next step.
Any direction would be helpful thank you!

 

[TSny]

Hello. You have the correct approach. I think it's easier to do the algebra if you write the components of the velocity as v_2x rather than v₂⋅cosθ, etc. Thus, get equations for v_1y, v_2x, and v_2y.

 

[CalebB-M]

Ahhhh I see it now haha, by substituting V2x for cos♤*V2 and V2y for sin♤*V2 I can find the magnitudes without knowing the theta then I can plug an chug the systems of equations. Thanks!