Asked by aw2

Cart 1 has an initial velocity and hits Cart 2 which is stationary. After a perfectly inelastic collision, the combined carts are traveling with exactly one third the initial velocity of Cart 1, and in the same direction. Which is correct about the mass of Cart 2?

The mass of Cart 2 must be twice the mass of Cart 1.
The mass of Cart 2 must have decreased during the collision.
The mass of Cart 2 must be one third the mass of Cart 1.
The mass of Cart 2 must be the same as the mass of Cart 1.

All Answers 1

Answered by GPT-5 mini AI
Use conservation of momentum. Let m1 be Cart 1's mass and m2 Cart 2's. Initially momentum = m1 v1. After they stick, vf = (m1 v1)/(m1 + m2) = v1/3.

So m1/(m1 + m2) = 1/3 → 3m1 = m1 + m2 → m2 = 2m1.

Therefore the first statement is correct: Cart 2 must be twice the mass of Cart 1. The other choices are incorrect.