Analyzing 2D Elastic Collisions with Varying Masses and Velocities

[poolec4]

Homework Statement

A 1.0-kg particle is moving in the +x direction at 4.0m/s when it collides elastically with a 4.0-kg particle moving in the −x direction at 1.0m/s After colliding the 1-kg particle moves off at 130 counterclockwise from the positive x-axis. Find the final speeds of both particles and the direction of the more massive one.

Homework Equations

m1*v1=(m1*v3*cos(ø3))+(m2*v4*cos(ø4))

0=(m2*v4*sinø4)-(m1*v3*sin(ø3))

m1*v1^2 = (m1*(v3)^2) + (m2*(v4)^2)

The Attempt at a Solution

(1 kg)(4i m/s) + (4 kg)(-1i m/s) = 0 ==> The total momentum=0

Is there some sort of trick that can be used for 2 dimensional elastic collisions when the masses and speeds swap? Also, since the total momentum is 0, can it be specified as a center-of-mass system, thus being able to use the scattering angle? Thanks in advance for any help!

 

[TSny]

Hello poolec4. Welcome to PF!

What is the total momentum vector after the collision?

What does that tell you about the magnitudes and the relative directions of the individual final momenta?