Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at speed 2v, while the second was traveling at speed v at an angle ϕ south of east (as indicated in the figure). After the collision, the two-car system travels at speed v final at an angle θ east of north. (Figure 1)

Find the speed v final of the joined cars after the collision.

Express your answer in terms of v and ϕ.