The propellant in a single stage sounding rocket occupies 60 % of its initial mass. If all of it is expanded instantaneously at an equivalent exhaust velocity of 3000 m/s, what would be the altitude attained by the payload when launched vertically?
The propellant in a single stage sounding rocket occupies 60 % of its initial mass. If all of it is expanded instantaneously at an equivalent exhaust velocity of 3000 m/s, what would be the altitude attained by the payload when launched vertically?(Neglect drag and assume acceleration due to gravity to be constant at 9.91\(\;m/s^{2}\).
Using the ideal rocket equation \[V=u_{e}ln\frac{m_{i}}{m_{f}}
\\\Rightarrow 3000\times ln\left ( \frac{m}{0.4m} \right )
\\\Rightarrow V=3000\times ln\left ( 2.5 \right )
\\\Rightarrow V=2748.87\;m/s\]
Altitude attended by the payload \[\frac{v^{2}}{2g}=\frac{2748.87^{2}}{2\times 9.91}
\\\approx 381\;km\]
