Elastic Collision Calculation: Determining Speed of Carts Post-Collision

The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision in an isolated system. For this system, we have two carts moving in the same direction (positive). Their total momentum before the collision will be equal to the momentum after the collision, as they stick together. Before the collision momentum (momentum = mass * velocity): Momentum of 3.00 kg cart = 3.00 kg * 4.00 m/s = 12.00 kg*m/s Momentum of 5.00 kg cart = 5.00 kg * 2.00 m/s = 10.00 kg*m/s Total initial momentum = 12 kg*m/s + 10 kg*m/s = 22 kg*m/s After the collision, the two carts stick together, thus their combined mass is (3.00 kg + 5.00 kg) = 8.00 kg. To find their speed (v) after the collision, we put this into the formula of momentum: Total final momentum = 8.00 kg * v Given that total initial momentum = total final momentum, we get: 22 kg*m/s = 8.00 kg * v Solving for v gives us: v = 22 kg*m/s / 8.00 kg = 2.75 m/s Therefore, the speed of the two carts after they collide and stick together is 2.75 m/s.