An open boxcar has a mass of 30,000 kg and is moving on a level railroad track at 4.00 m/s. 1,000 kg of water falls straight down into the boxcar. The speed of the boxcar after the water falls into it is
A) 7.01 m/s.
B) 6.55 m/s.
C) 5.02 m/s.
D) 3.87 m/s.
E) 2.89 m/s.

Question

Quizplus · Accepted Answer

The initial momentum of the boxcar and water system is:
p initial = mv = (30,000 kg + 1,000 kg) × 4.00 m/s = 1.24 × 10^5 kg m/s

After the water falls into the boxcar, the momentum is:
p final = (30,000 kg + 1,000 kg) × v
where v is the final velocity of the system.

Conservation of momentum requires that:
p initial = p final

Therefore:
(30,000 kg + 1,000 kg) × 4.00 m/s = (30,000 kg + 1,000 kg) × v

Solving for v, we get:
v = 3.87 m/s

Therefore, the speed of the boxcar after the water falls into it is 3.87 m/s. The correct answer is (D).

An Open Boxcar Has a Mass of 30,000 Kg and Is