# Speed and Momentum Calculation in Cart Collision

Before the collision, cart A was moving at a speed of 9.25 m/s with a mass of 72.0 kg, while cart B was moving at a speed of 7.15 m/s with a mass of 55.0 kg. After the collision, cart A slowed down to 6.15 m/s.

In order to find the final speed of cart B after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Mathematically, we can represent this as:

\(m_{A}v_{A} + m_{B}v_{B} = m_{A}v'_{A} + m_{B}v'_{B}\)

Where:

\(m_{A}\) = mass of cart A

\(v_{A}\) = initial velocity of cart A

\(m_{B}\) = mass of cart B

\(v_{B}\) = initial velocity of cart B

\(v'_{A}\) = final velocity of cart A

\(v'_{B}\) = final velocity of cart B (the value we need to find)

By substituting the given values into the equation, we can calculate the final speed of cart B:

\(72.0 \times 9.25 + 55.0 \times 7.15 = 72.0 \times 6.15 + 55.0 \times v'_{B}\)

\(66.0 + 394.25 = 441.6 + 55.0 \times v'_{B}\)

\(460.25 = 441.6 + 55.0 \times v'_{B}\)

\(v'_{B} = \dfrac{460.25 - 441.6}{55.0}\)

\(v'_{B} = \dfrac{18.65}{55.0}\)

\(v'_{B} = 0.339 \, \text{m/s}\)

Therefore, the final speed of cart B after the collision is 11.21 m/s.