Final answer:
The final speed of the train car after the boulder is dropped can be found by applying the conservation of momentum principle, with the resulting speed being less than the initial speed of 10 m/s due to the increased mass.
Step-by-step explanation:
The question is asking to find the speed of an empty train car immediately after a 3000-kg boulder is dropped into it, given that the car was initially moving at 10 m/s and has a mass of 2.0 × 10⁴ kg. To solve this, we use the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces are acting on it.
Before the boulder is dropped, the momentum of the train car is:
Initial momentum of train car = mass of car × velocity of car = (2.0 × 10⁴ kg)(10 m/s) = 2.0 × 10⁵ kg·m/s
Since the boulder is dropped vertically, its initial horizontal momentum is 0. After the boulder is dropped, the total mass of the car plus boulder is (2.0 × 10⁴ kg + 3000 kg).
Using the conservation of momentum:
Initial momentum = Final momentum
(2.0 × 10⁵ kg·m/s) = (2.0 × 10⁴ kg + 3000 kg) × final velocity
Solving for the final velocity gives:
final velocity = (2.0 × 10⁵ kg·m/s) / (2.0 × 10⁴ kg + 3000 kg)
Therefore, the final velocity is less than the initial velocity of 10 m/s due to the added mass of the boulder.