- #1

- 59

- 9

Typical chemical fuels yield exhaust speeds of the order of 10

^{3}m/s. Let us imagine we had a fuel that gives v

_{0}= 3 × 10

^{5}m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?

I derived the equation in the first part of the problem:

\begin{equation}

v - v_0 = v_e \ln(\frac{m_0}{m})

\end{equation}

Solving for the initial mass, m, yields

\begin{equation}

m_0 = me^{\frac{\Delta v}{v_e)}}

\end{equation}

I plug in that.

0.1c = 3.0*10^7

v

_{0}= 3.0*10^5

v

_{e}e = 1.0*10^3

v - v

_{0}= 3.0 *10^7 - 3.0*10^5 = 2.97*10^7

m = 1000 kg

I plug in these numbers and I am getting infinity. What am I doing wrong?

Thanks!