A 28,500 kg open railroad car, initially coasting at 0.95 m/s with negligible friction, passes under a hopper that dumps 122,500 kg of scrap metal into it. What is the final speed, in meters per second, of the loaded freight car?

Using the Law of Conservation of Momentum, which states the total momentum of an isolated system is constant if no external forces act on it, we can equate the initial and final momenta of the system to find the final speed of the loaded freight car.

Explanation:

The physics concept in this question is the Law of Conservation of Momentum, which states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of a moving railroad car and the scrap metal that's falling into it from the hopper. The initial momentum of the system is the momentum of the empty railroad car coasting at a speed of 0.95 m/s, which is equal to its mass (28500 kg) times its speed (0.95 m/s). Likewise, the final momentum of the system is the momentum of the loaded railroad car, which is equal to the total mass (28500 kg for the empty car plus 122500 kg for the scrap metal) times its final speed, which we're trying to find.

Since the Law of Conservation of Momentum states the initial and final momenta of the system are equal, we can find the final speed of the loaded freight car by equating the initial and final momenta and solving for the final speed. Doing so, we get: (28500 kg * 0.95 m/s) = (28500 kg + 122500 kg) * final_speed.

Solving this equation for final_speed, we get: final_speed = (28500 kg * 0.95 m/s) / (28500 kg + 122500 kg), which gives us the final speed in meters per second.

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