Analyzing an Elastic Collision in 2D: Solving for Speed and Angle

[fliinghier]

Homework Statement

there are two masses, the smaller sitting still, and the larger with 5 times the mass of the smaller hits it going 12 m/s. the smaller rebounds at an 80 degree angle from the direction of the original mass. the collision is elastic. find the speed of both objects and the angle of the larger one after the collision.

Homework Equations

1/2mv^2 (KE, which is conserved)
mv (momentum, which is conserved)

The Attempt at a Solution

so far i have tried using sin and cos of theta and 80 degrees to find equivalent equations using momentum(5V2sin(theta)=V1sin(80) and 60=5V2cos(theta)+V1cos(80)) and then i tried to plug variables into the KE equation or solve the equations simultaneously.

 

[Doc Al]

You are on the right track. Try this: Use the momentum equations to find V2 in terms of V1. Then plug that into the KE equation. (Hint: Take advantage of the trig identity $\sin^2\theta + \cos^2\theta = 1$.)

 

[fliinghier]

after trying this way again i got stuck (again) when i reached the following:

720=(V1^2)(1+(.970/(sin(theta))^2))

 

[Doc Al]

Use the hint I gave to eliminate theta before plugging into the KE equation.

 

[fliinghier]

thanks i think i got it now.