A stationary two stage rocket with initial mass of $16000 \mathrm{~kg}$, carrying a payload of $1000 \mathrm{~kg}$, is fired in a vertical trajectory from the surface of the earth. Both the stages of the rocket have same specific impulse, $\boldsymbol{I}_{s p},$ of $300 \mathrm{~s}$ and same structural coefficient of $0.14 .$ The acceleration due to gravity is $9.8 \mathrm{~m} / \mathrm{s}^{2}$. Neglecting drag and gravity effects and considering both the stages with same payload ratio, the terminal velocity attained by the payload in $m / s$ is____________

A stationary two stage rocket with initial mass of $16000 \mathrm{~kg}$, carrying a payload of $1000 \mathrm{~kg}$, is fired in a vertical trajectory from the surface of the earth. Both the stages of the rocket have same specific impulse, $\boldsymbol{I}_{s p},$ of $300 \mathrm{~s}$ and same structural coefficient of $0.14 .$ The acceleration due to gravity is $9.8 \mathrm{~m} / \mathrm{s}^{2}$. Neglecting drag and gravity effects and considering both the stages with same payload ratio, the terminal velocity attained by the payload in $m / s$ is____________

An aircraft is flying at Mach 3.0 at an altitude where the ambient pressure and temperature are 50 $k P a$ and $200 K$ respectively. If the converging-diverging diffuser of the engine (considered isentropic with ratio of specific heats, $\gamma=1.4$ and specific gas constant $\mathrm{R}=287 \mathrm{~J} / \mathrm{kgK}$ ) has a throat area of $0.05 \mathrm{~m}^{2},$ the mass flow rate through the engine in $\mathrm{kg} / \mathrm{s}$ is

(A) 197

(B) 232

(C) 790

(D) 157

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