Question

A car with a mass of 1700 kg is traveling directly northeast (45 degrees between north and east) at a speed of 14m/s (31mph), and collides with a smaller car with a mass of 1300kg that is traveling directly south at a speed of 18m/s (40mph). The two cars stick together during the collision. With what speed and direction does the tangled mess of metal move right after the collision?

Answer 1

do conservation of momentum in NS, and EW directions. Notice the final velocity then will be a vector you can determine the angle and magnitude from.

Answer 2

M1*V1 + M2*V2 = M1*V + M2*V.
1700*14[45o] + 1300*18[270o]=1700V+1300V
Divide both sides by 100:
17*14[45] + 13*18[270] = 17V + 13V.
238[45] + 234[270] = 30V.
168.3+168.3i -234i = 30V.
168.3 - 65.7i = 30V.
180.7[-21.3o] = 30V.
V = 6.0 m/s[-21.3] = 6.0m/s[21.3o] S. of
E.