A1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. the two cars stick together after the collision. what is the direction of motion of the cars after collision?

Let's take the positive x-direction towards east and the positive y-direction towards south. The momentum must be  conserved on both directions, after the collision. On the x-direction, initially we have only momentum from car 1, while on the y-direction initially only car 2 contributes to the total momentum of the system. After the collision, the two cars will move together with a total mass (m1+m2) and with final velocity vf, which can be decomposed on both directions. All of this translates into the equations:
(1)
(2)
where , ,  and .  and  are the components of the final velocity on both axes x and y.

By dividing equation (2) by (1), we get:


And the tangent of this ratio gives exactly the angle of the velocity vf in the south-east direction, with respect to the positive x-axis, so it gives us the direction of the final velocity:

Velocity is the speed of an object in a certain direction so you'd need to know speed and direction