Use the rocket formula v = s In(Mfuel/Mpayload -1) to find the ratio Mfuel/Mpayl

Question

Use the rocket formula v = s In(Mfuel/Mpayload -1) to find the ratio Mfuel/Mpayload in the case that v = 100s. This could correspond to the case of a chemical fuel with exhaust velocity s = 3km/s and a final velocity after fuel exhaustion of v = 300km/s which is only 0.1% of light speed. If your rocket weighs 100 tons how much fuel would you need in tons? Use the rocket formula v = s In(Mfuel/Mpayload -1) to find the ratio Mfuel/Mpayload in the case that v = 100s. This could correspond to the case of a chemical fuel with exhaust velocity s = 3km/s and a final velocity after fuel exhaustion of v = 300km/s which is only 0.1% of light speed. If your rocket weighs 100 tons how much fuel would you need in tons?

Explanation / Answer

v = s In(Mfuel/Mpayload -1)

ln(Mf/Ml -1) = v/s

s = 3km/s

v = 300km/s

ln(Mf/Ml -1) = 100

Mf/Ml -1 = e100

Mf = Ml(e100 +1)

Mf = Ml(2.69 x 1043)

Mf = 100 x103 x 2.69 x 1043kg

Mf = 2.69 x 1048kg

well thats the answer i am getting as per the question but i some how feel some thing is mis typed in the question as this value is too large

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