A sedan weighing 4000 pounds travelling at 30mph collides head on with a compact car weighing 2000 pounds and travelling in the opposite direction at 45 mph. What is the resultant velocity of the combined vehicles?

Answer 1

Assume that the two cars stick together and appply that law of conservation of momentum.
4000*30 -2000*45 = 6000*Vfinal
Vfinal = (1.2*10^5 - 0.9*10^5)/6000
= 5.0 mph (in the original drection of the 4000 lb car).

I did not have to convert mass to slugs or velocities to ft/sec, because I used the same units for each term (lbmass*miles/h)