A rocket having initial massmkg is launched vertically from the ground. the rocket expels gas at a constant rate of_{0}akg/s and at a constant velocitybm/s relative to the rocket. Assuming that air resistance is proportional to the rocket velocityv(t)with prop. constantk, find the velocity of the rocket at t=6s, and after the massmkg of gas is used up._{g}

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.