How much fuel is needed to reach a specific velocity in rocket propulsion?

[car202]

Homework Statement

The space shuttle, with an initial mass M = 2.41E+6 kg, is launched from the surface of the Earth with an initial net acceleration a = 26.1 m/s2. The rate of fuel consumption is R = 6.90E+3 kg/s. The shuttle reaches outer space with a velocity of vo = 4632 m/s, and a mass of Mo = 1.45E+6 kg. How much fuel must be burned after this time to reach a velocity vf = 5158 m/s?

 

[mgb_phys]

At least take a guess at what you need to know !

 

[car202]

well i got some answer..but all of them were wrong. Ve(dm/dt) = M(dv/dt), Vf-Vi= Ve(ln(Mi/Mf)...As it reaches outer space, I got acceleration of 43.38 and since gravity is not acting, added 9.81 to get 53.19. I set this to dv/dt. Got Ve. And plugged into formula...but did not work. What's wrong?

 

[car202]

My only question is, on equation Ve(dm/dt) = M(dv/dt), how do we get dv/dt? I really don't get it..Is it constant?

 

[car202]

Oops, I solved the problem! FYI answer is 5.96×10^4 kg.