Calculating Post-Collision Speed: Inelastic Collision of Carts with Mixed Velocities

This problem can be solved by using the principle of the conservation of linear momentum, which states that if no external forces act on a system, its total momentum remains constant. The initial momentum of the system is the sum of the momenta of the two carts before the collision. The final momentum is the product of the combined mass of the carts (due to them sticking together) and their final velocity. Setting the initial momentum equal to the final momentum and solving for the final velocity, you get: Initial momentum = (3.00 kg * 4.00 m/s) + (5.00 kg * 2.00 m/s) = 22.00 kg*m/s Final momentum = final velocity * total mass = final velocity * (3.00 kg + 5.00 kg) So, 22.00 kg*m/s = final velocity * 8.00 kg, which gives us final velocity = 22.00 kg*m/s / 8.00 kg = 2.75 m/s So, the correct option is: B. 2.75 m/s