A rocket ascends from rest in Earth's gravitational field, by ejecting exhaust with constant speed u. Assume that the rate at which mass is expelled is given by dm/dt = −γm where m is the instantaneous mass of the rocket and γ is a constant; and that the rocket is retarded by air resistance with a force mbv where b is a constant.
Determine the velocity of the rocket as a function of time. Here is a hint: The terminal velocity is ( γu−g )/b.
Calculate the time when the velocity is one-half of the terminal velocity.
Data: u = 31.9 m/s; b = 1.2 s−1.
The Attempt at a Solution
I got the diff eq down to:
I'm not quite sure what I am doing wrong, I divide by -(g+bv)
then solve from there to get -b*ln(g+bv)=uγt, but for some reason I dont think this is correct. Help, thanks.