Final answer:
In order for the first cart to come to a stop after an elastic collision with the second cart, the two carts must have the same mass and opposite velocities. The mass of the second cart should be 300 kg and its initial velocity should be -3 m/s.
Step-by-step explanation:
In order for the first cart to come to a stop after an elastic collision with the second cart, the two carts must have the same mass. This is because the momentum of the system is conserved in an elastic collision, meaning that the initial momentum of the first cart must be equal in magnitude but opposite in direction to the final momentum of the combined carts.
If the initial velocity of the first cart is 3 m/s and its mass is 300 kg, then the initial momentum is given by: Momentum = mass x velocity = 300 kg x 3 m/s = 900 kg * m/s.
To bring the first cart to a stop, the second cart must have the same mass of 300 kg and an initial velocity in the opposite direction (-3 m/s). This will result in a final momentum of 900 kg * m/s in the negative direction, causing the first cart to come to a stop.