what is the velocity of the final stage?

Question

The 5,000 kg final stage of spaceship ejects the 10,000 kg second stage. Before ejection, the two stages together travel with a velocity of 200 m/s. If after ejection, the second stage travels 80 m/s opposite the direction of its initial motion, what is the velocity of the final stage?; please show the formula that u used. thanks

Answer 1

Momentum conservation can solve this problem.
We may not use energy conservation, since the spaceship must use some energy to lunch this ejection, and we do not know this energy the spaceship used.
Let the final velocity of the final stage to be v, we have:
(5000kg + 10000kg)*200 m/s = 10000kg*(-80m/s) + 5000kg*v
Please solve v.