Two cars crash into each other at an intersection on a very icy road. One 3,000 lb car is traveling 45 mph NW. The other, weighing 2,000 lb, is traveling 30 mph E. After the collision, their bumpers lock together. What is the velocity of the wreck as it slides off the road ?
Add the momentum vectors and divide by the combined mass.
North component of momentum:
= 3000 * 45 cos 45
= 9.55*10^4 mph*lb
East component of momentum:
= -3000*45sin45 + 2000*30
= -9.546*10^4 + 6.00*10^4
= -3.546*10^4 mph*lb
The momentum magnitude is
sqrt[(9.546)^2 +(-3.546)^2]*10^4
= 1.018*10^5 mph*lb
Final velocity is that divided by 5000 lb, or 20.4 mph
If you need the direction, use the ratio of momentum components as the tangent of the angle.
It is about 20 degrees west of north.