**Collision at an Angle**

To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass *m*, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2*v*, while the second was traveling in a southeastern direction at an angle *ϕ* with respect to the east-west direction and at a speed *v*. After the collision, the two-car system travels in a northeastern direction at an angle *θ* with respect to the north-south direction and at a speed *v *final.

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

Express your answer in terms of *v* and *ϕ*.

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