Velocity Puzzle: Solving for the Post-Collision Speed of Inelastically Colliding Carts

To solve this problem, we need to use the principle of conservation of momentum. The momentum of an isolated system remains constant if no external forces act on it. The initial momentum of the system is the sum of the momentums of the 3-kg cart and the 5-kg cart before the collision. The final momentum of the system is the momentum of the two carts after they have stuck together. The momentum (p) before the collision is: p_initial = mass_1 * velocity_1 + mass_2 * velocity_2 p_initial = 3.00 kg * 4.00 m/s + 5.00 kg * 2.00 m/s = 12 kg*m/s + 10 kg*m/s = 22 kg*m/s Momentum is conserved so the momentum (p) after the collision is also: p_final = p_initial = 22 kg*m/s After, the collision the two carts stick together and move with the same velocity (v_final). The combined mass of the two carts is 3.00 kg + 5.00 kg = 8.00 kg. We can find v_final by dividing the momentum after the collision by the total mass: v_final = p_final / (mass_1 + mass_2) v_final = 22 kg*m/s / 8.00 kg = 2.75 m/s The speed of the two carts after the collision is 2.75 m/s.