# Final Velocities of Carts After Elastic Collision

## Calculation of Velocities Post-Collision

**Given data:**

- Mass of cart 1 (m): m
- Velocity of cart 1 pre-collision: v
- Mass of cart 2: 9m
- Velocity of cart 2 pre-collision: 0 (at rest)
- Velocity of cart 1 post-collision: v/10
- Velocity of cart 2 post-collision: 9v/10

## Explanation:

The velocity of both carts after the collision can be calculated using the conservation of momentum principle in an elastic collision.

Before the collision, the total momentum of the system is the momentum of cart 1, which is m*v.

After the collision, the total momentum of the system is equal to the combined momentum of both carts, denoted as v1 and v2 for carts 1 and 2 respectively.

By applying the conservation of momentum equation, we can derive the velocities post-collision:

v1 = (mv) / (m + 9m) = v / 10

v2 = (9mv) / (m + 9m) = 9v / 10

Therefore, after the collision, cart 1 will have a velocity of v/10, and cart 2 will have a velocity of 9v/10.