(Solved): (C2M.3) Suppose that a cart with mass \( m \) and low-friction wheels is moving to the right with a ...

(C2M.3) Suppose that a cart with mass \( m \) and low-friction wheels is moving to the right with an initial speed \( \left|\vec{v}_{0}\right| \) just before it hits a cart with mass \( M \) at rest. After the collision, the first cart rebounds to the left with a speed of (3/5)| \( \vec{v}_{0} \mid \) and the other cart moves to the right with a speed of \( (2 / 5)\left|\vec{v}_{0}\right| \). Assume that each cart receives zero net momentum from any external interactions (such as gravitational and contact interactions) other than their collision interaction. (a) What impulses did the collision interaction deliver to each cart? Express the impulse's directions as "left" or "right" and their magnitudes as multiples of \( m\left|\vec{v}_{0}\right| \). (Hint: Draw some momentum arrows.) (b) Use this information to calculate \( M \) as a multiple of \( m \).