Question

A 2,500-kg car moving east at 10.0 m/s collides with a 3,000-kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 35.0 degrees north of east and at a speed of 5.55 m/s. Find the speed of the 3,000-kg car before the collision.
__________ m/s north

Answer 1

If the only momentum in the East direction is the 2500Kg car, then we can assume that, after the collision, the only momentum of the two cars is still this, which will not change.

the momentum in the east= 2500 kg x 10 m/s = 25000 kg m/s

So now we can split up the collided mass' velocity into its components parts, allowing a right- angled triangle to be drawn, where 25000 is the the adjacent side to the angle 35.0, and the momentum in the north direction is the opposite

therefore we know, from trigonometry that

tan 35 = opposite/ adj = opp/ 25000

0.7 = opp/25000
17505 = opp

therefore the momentum of the mass in the north direction is 17505

since momentum= mass x velocity

17505= 3000 x velocity

17505/ 3000 = 5.83 m/s