Car A(1750kg) traveling due south and car B (1450kg)due east. They reach the same intersection at the same time and collide. The cars lock together and move off at 35.8km/h[E31.6degS]. What was the velocity of each car before the collided?

Question

I tried this question using the law of momentum i keep getting 65km/h but the answer is supposed to be 34.3km/h for car a and for car b 67.3km/h. Is there some other method to do this?

Answer 1

They already tell you the original DIRECTION of each car's motion.

All of the combined momentum in the south direction comes from car A's initial momentum.

All of the combined momentum in the east direction comes from car B's initial momentum. Putting that in equation form:

1750*Va = 35.8*3200*sin31.6

1450*Vb = 35.8*3200*cos31.6

Va = 34.3 km/h etc

It was not necessary to convert velocity to m/s units, to get the answer in the same km/h units