Suppose the initial mass of the rocket at liftoff is m including fuel, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity vsube (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation
v(t)=-gt-vsube ln[(m-rt)/m] where g is the acceeration due to gravity and t is not too large. If g is 9.8 m/s^2, m=30000 kg, r=160 kg/s, and vsube=3000 m/s, find the height of the rocet one minute after liftoff.
So I know I need to integrate from 0 to 1 (I think), but how in the world do I do that with this equation.