Final answer:
To calculate the final velocity of two boxes that collide and stick together, we can use the principle of conservation of momentum. By equating the initial momentum of the larger box to the final momentum of the combined system, we can find the final velocity. In this case, the final velocity of the two boxes together would be 5/12 m/s.
Step-by-step explanation:
To determine the final velocity of the two boxes after collision, we can use the principle of conservation of momentum. The initial momentum of the larger box is calculated by multiplying its mass (let's call it mA) by its initial velocity (12 m/s). The initial momentum of the smaller, stationary box (mass mB) is zero since it's not moving. After the collision, the two boxes stick together and move as one. The final momentum of the combined system is equal to the sum of the initial momenta of the two boxes. The final velocity of the system can be calculated by dividing the final momentum by the combined mass of the two boxes, which is mA + mB.
Let's apply this to the given scenario. The larger box has an initial velocity of 12 m/s and a final velocity of 5 m/s. The smaller box is initially stationary, so its initial velocity is zero. Let's assume that both boxes have the same mass, m. Using the principle of conservation of momentum, we can set up the equation: (m * 12 m/s) + (0) = (m + m) * 5 m/s. Simplifying this equation, we get: 12m = 10m. Dividing both sides by 10, we find that m = 6/5. Therefore, the combined mass of the two boxes is (6/5 + 6/5) = 12/5. Finally, dividing the final momentum (which is the combined mass times the final velocity of 5 m/s) by the combined mass of 12/5, we find that the final velocity of the system is 5/12 m/s.