Speed of a railroad car (Physics)?

Question

Changing Mass. A railroad hopper car filled with sand is rolling with an initial speed of 15.0 m/s on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass of the car plus sand is 85,000 kg. The hopper door is not fully closed so sand leaks out the bottom. After 20 minutes, 13,000 kg of sand has leaked out.

Then what is the speed of the railroad car?

Answer 1

m1v1=m2v2
85000*15=72000*X

X=17.71 m/s

So the new speed is 17.71 m/s. This is due to conservation of momentum.

Answer 2

This is a very nice trick question. Ignoring frictional forces, the speed of the car is UNCHANGED. Imagine riding on the hopper car. You couldn't slow it down by dropping sand on the ground could you? So the answer is the final speed is 15.0 m/s, same as the inital speed...

Addendum:
Since a couple people have mentioned conservation of momentum, I should explain why the unchanging speed doesnt violate it. It makes no difference if the sand falls slowly, as stated in the problem, or quickly. So imagine the sand being a "block" shape which drops all at once from the bottom of the train. While the block of sand is falling to the ground, the total momentum is unchanged. When the block of sand hits the ground, it stops moving so its momentum becomes zero. Momentum is conserved because the sands momentum is transfered to the earth, which will move (however microscopically).
Here is another way to look at it. For the boxcar to slow down, there MUST be a force acting on it, against its direction of motion. Just dropping the sand to the ground doesn't create any force on the car, so it cant change its motion.

Answer 3

we have to look at momentum in and different way because mass isn't constant. You can't ignore the change in mass and it isn't a trick question.

momentum must still conserved
m1*v1=85E3*15=(85000-13000)*v2

v2=17.7 m/s