Question

Solve this:
Q.17. During the rocket propulsion, gases ejecting with velocity 1 km/s relative to rocket. The rate of fuel consumption is $\frac{m}{10}$ kg/s, where m is the instantaneous mass of the rocket. If air resistance varies according to equation f = 0.15 mv, then terminal velocity of the rocket is :-
(1) 300 m/s
(2) 600 m/s
(3) 7.92 km/s
(4) 11.2 km/s

Answer 1

Dear Student,



$$\begin{gathered} P=mv \\ \frac{dp}{dt}=v\frac{dm}{dt} \\ F=\frac{mv}{10} \\ v=1000m/s \\ F=100mN\hspace{0.17em} \\ 0.15mv+mg=100m \\ v=\frac{90}{0.15}=600m/s \\ Regards \end{gathered}$$