The momentum of a moving object is given by:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Let the y-axis point to the north and the y-axis point to the left.

**(a) **

Momentum before collision = momentum after collision

m_{1}v_{1} + m_{2}(0) = (m_{1} + m_{2}) v cos θ

In this problem we will consider the collision of two cars initially moving at right angles. We assume that after the collision the cars stick together and travel off as a single unit. The collision is therefore completely inelastic. Two cars of masses m_{1} and m_{2} collide at an intersection. Before the collision, car 1 was traveling eastward at a speed of v_{1}, and car 2 was traveling northward at a speed of v_{2}. (Figure 1) After the collision, the two cars stick together and travel off in the direction shown.

(a) Write the momentum conservation equation for the east-west components. Express your answer in terms of v_{1}, m_{1}, m_{2}, θ, and v, the speed of the 2-car unit after the collision.

(b) Write the momentum conservation equation for the north-south components. Express your answer in terms of v_{1}, m_{1}, m_{2}, θ, and v, the speed of the 2-car unit after the collision.

(c) Find the magnitude of v , that is, the speed v of the two-car unit after the collision. Express your answer in terms of v_{1}, m_{1}, m_{2}, and v_{2}.

(d) Find the tangent of the angle. Express your answer in terms of v_{1}, m_{1}, m_{2}, and v_{2}.