Inelastic collision at an angle

[powerofsamson]

Homework Statement

What is the angle theta with respect to north made by the velocity vector of the two cars after the collision?
Express your answer in terms of phi. Your answer should contain an inverse trigonometric function.

the cars are both of mass m.

Homework Equations

I already found v_final for the first part of the question. The hint says that tan theta = v_final in the x direction / v_final in the y direction.

The Attempt at a Solution

This equation is wrong: (m(2v)+m(v)sin(phi))/(2mv_final cos(theta)) = tan(theta)

 

[Astronuc]

Write the momentum equations in x and y.

Note that the y-component of momentum of the car at an angle is negative (opposite) that of the car traveling north at 2v.

 

[powerofsamson]

For x I have v_finalx = (2m)v_final * cos (phi). For y i have v_finaly = (2m)v_final * sin (phi). This would mean that tan (theta) = cos (phi)/sin(phi). I've already tried atan (cos(phi)/sin(phi).

 

[soupastupid]

how do i do the first part?
my question is asking me the speed of v_final

i think its sqrt ( (v_final * cos (phi))^2 + (2v_final - v_final * sin (phi) ) ^2 )