# Collision at an angle

Two cars, both of mass , collide and stick together. Prior to the collision, one car had been traveling north at speed , while the second was traveling at speed at an angle south of east (as indicated in the figure). After the collision, the two-car system travels at speed at an angle east of north.

What is the angle with respect to north made by the velocity vector of the two cars after the collision?

I have already tried tan(theta)=cos(phi)/(2-sin(phi)) and arctan(cos(phi)/(2-sin(phi)) and tan(cos(phi)/(2-sin(phi)) but none seem to be the right answer

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Delphi51
Homework Helper
Make two headings for "north/south" and "east/west".
Under each write "momentum before = momentum after".
Use only the component of velocity in the direction specified by the heading in each mv calculation. You should be able to calculate the two components of velocity for the attached vehicles. Then you can use trigonometry to find their combined velocity, magnitude and direction.

soooo for x I have v_finalx = (2m)v_final * cos (phi) and 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)....right?

Delphi51
Homework Helper
Sorry, I am not quite able to see your final answers. Certainly the m should have canceled out somewhere along the line so the answers will have the units of velocity rather than momentum. Also the initial velocities for the two cars should appear in the expressions for the final velocities. Maybe show your work so I can follow . . .