Understanding Elastic Collision: How Fast Will Cart B Move?

In an elastic collision, both kinetic energy and momentum are conserved. Since one cart comes to a stop after the collision, all its kinetic energy is transferred to the other cart, resulting in its movement. Here's how you can calculate the speed of cart B after the collision:

Explanation:

Momentum Conservation: Before the collision, the total momentum of the system is the sum of the momentum of cart A and the momentum of cart B. Since cart A is moving and cart B is at rest, the initial total momentum is 1 kg * 2 m/s = 2 kg*m/s.

After the collision, cart A is stationary, so its momentum is 0. According to the law of conservation of momentum, the total momentum of the system remains the same. Therefore, the momentum of cart B after the collision is also 2 kg*m/s.

Final Velocity of Cart B: To find the final velocity of cart B, use the formula for momentum:

Final momentum of cart B = mass of cart B * final velocity of cart B

Since the mass of cart B is 1 kg and the total momentum of the system is 2 kg*m/s, the final velocity of cart B can be calculated as:

2 kg*m/s = 1 kg * final velocity of cart B

Final velocity of cart B = 2 m/s

Therefore, after the perfectly elastic collision, cart B will move at a speed of 2 m/s.