A rocket having initial mass m_{0} kg is launched vertically from the ground. the rocket expels gas at a constant rate of a kg/s and at a constant velocity b m/s relative to the rocket. Assuming that air resistance is proportional to the rocket velocity v(t) with prop. constant k, find the velocity of the rocket at t=6s, and after the mass m_{g} kg of gas is used up.
Solution:
Let M be mass at any time t
M(t)' = -(at^{2})/2 + c
Solving gives M = m_{0 }- (at^{2})/2
After this I'm not sure how to use the forces. Can someone help with the next steps please? Thanks.