Question

A 1250-kg compact car is moving with velocity v1 =36.2i^+12.7j^m/s. It skids on a frictionless icy patch and collides with a 448-kg hay wagon moving with velocity v2=13.8i^+10.2j^m/s.
If the two stay together, what is their velocity?
Express your answer in meters per second in terms of i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer.

Answer 1

Momentum is conserved, so the sum of the separate momenta of the car and wagon is equal to the momentum of the combined system:

(1250 kg) ((36.2 i + 12.7 j ) m/s) + (448 kg) ((13.8 i + 10.2 j ) m/s) = ((1250 + 448) kg) v

where v is the velocity of the system. Solve for v :

v = ((1250 kg) ((36.2 i + 12.7 j ) m/s) + (448 kg) ((13.8 i + 10.2 j ) m/s)) / (1698 kg)

v ≈ (30.3 i + 12.0 j ) m/s