Question

exhaust gas from a rocket ship is released at a speed of 1000 m/s so that the craft from 100m/s to 200 m/s .How much fuel is necessary to complete this acceleration,if the mass of the ship was originally 10000 kg?​

Answer 1

Answer:952 kg

Explanation:

By law of conservation of Momentum

$m\frac{dv}{dt}=-v_{rel}\frac{dm}{dt}$

rearranging we get

$dv=-v_{rel}\frac{dm}{m}$

$\int_{100}^{200}dv=-v_{rel}\int_{m_i}^{m_f}\frac{dm}{m}$

$(v)_{100}^{200}=-v_{rel}\times [\ln (m)]_{m_i}^{m_f}$

$(200-100)=(1000)\times (\ln (\frac{m_f}{m_i}))$

$m_f=m_ie^{-0.1}$

$m_f=10000\times 0.9048$

$m_f=9048\ kg$

Difference between initial and final mass is the amount of fuel

$m=m_i-m_f$

$m=10000-9048=952\ kg$