The acceleration of an upward rocket is given by the following differential
equation:
\frac{dv}{dt} = \frac{uq}{m_0 - qt} - g,
where $m_0$ is initial mass of rocket at $t = 0$ (kg), $q$ is rate at which fuel is
expelled (kg/s) and $u$ is velocity at which the fuel is being expelled (m/s).
Given the initial mass of the rocket is 100,000 kg, the rocket expels fuel
at a velocity 1400m/s at a consumption rate of 1500 kg/s and $g = 9.81$
(m/s²). Estimate the velocity of the rocket till time $t = 5$ with $\Delta t = 1$ and
$v_0 = 0$. If the exact solution is $v(t) = u \ln\left(\frac{m_0}{m_0 - qt}\right) - gt$, find the absolute
errors.
