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

AI Thread Summary
The discussion revolves around calculating the fuel required for a rocket to achieve a specific velocity, focusing on the space shuttle's parameters. The shuttle has an initial mass of 2.41 million kg and reaches an initial velocity of 4632 m/s, needing to attain a final velocity of 5158 m/s. The user initially struggled with the equations related to thrust and acceleration, particularly how to derive dv/dt. After some calculations and adjustments, they found that the amount of fuel needed to reach the desired velocity is approximately 5.96×10^4 kg. The conversation highlights the complexities of rocket propulsion calculations and the importance of understanding the underlying physics.
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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?
 
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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?
 
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?
 
Oops, I solved the problem! FYI answer is 5.96×10^4 kg.
 

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