Final answer:
The maximum mass of grain the 2000-kg railway freight car can accept to maintain a speed of no less than 3.0 m/s, based on the conservation of momentum, is 750 kg.
Step-by-step explanation:
To determine the maximum mass of grain that the 2000-kg railway freight car can accept without dropping below a speed of 3.0 m/s, we use the principle of conservation of momentum. The initial momentum of the empty car is its mass times its initial velocity (2000 kg × 4.4 m/s). Since no external forces are mentioned, the final momentum of the car after loading must be the same. However, the final velocity should not go below 3.0 m/s.
Calculation:
Initial momentum = 2000 kg × 4.4 m/s = 8800 kg·m/s
Final momentum = (2000 kg + m) × 3.0 m/s = 8800 kg·m/s
Solving for m (the mass of grain), we get:
m = ·(8800 kg·m/s)/(3.0 m/s) - 2000 kg
m = 2933.33 kg - 2000 kg
m = 933.33 kg
Since the options provided are in increments of 250 kg and 933.33 kg is closest to 750 kg within the provided options, the maximum mass of grain that can be accepted without the speed dropping below 3.0 m/s is 750 kg, which is option (b).