Calculating the Final Speed of Two Colliding Carts: Inelastic Collision Scenario

To find the speed of the carts after colliding, you can use the principle of conservation of momentum. The total momentum before the collision should equal the total momentum after the collision. The total initial momentum (p_initial) can be calculated by adding the momentum of each cart: p_initial = (mass of cart 1 * velocity of cart 1) + (mass of cart 2 * velocity of cart 2) p_initial = (3.00 kg * 4.00 m/s) + (5.00 kg * 2.00 m/s) p_initial = 12.00 kg*m/s + 10.00 kg*m/s p_initial = 22.00 kg*m/s Since the carts stick together after colliding, their final momentum (p_final) will be: p_final = (mass of cart 1 + mass of cart 2) * velocity p_final = p_initial So, their final velocity (v) can be calculated as: v = p_final / (mass of cart 1 + mass of cart 2) v = 22.00 kg*m/s / (3.00 kg + 5.00 kg) v = 22.00 kg*m/s / 8.00 kg v = 2.75 m/s. So, the speed of the two carts together after the collision is 2.75 m/s.