Question

A \(5000 \mathrm{~kg}\) rocket is set for vertical firing. The exhaust speed is \(800 \mathrm{~m} \mathrm{~s}^{-1}\). To give an initial upward acceleration of \(20 \mathrm{~m} \mathrm{~s}^{-2}\), the amount of gas ejected per second to supply the needed thrust will be \(\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)\)
(a) \(185.5 \mathrm{~kg} \mathrm{~s}^{-1}\)
(b) \(187.5 \mathrm{~kg} \mathrm{~s}^{-1}\)
(c) \(127.5 \mathrm{~kg} \mathrm{~s}^{-1}\)
(d) \(137.5 \mathrm{~kg} \mathrm{~s}^{-1}\)

Answer 1

Correct option (b) \(187.5 \mathrm{~kg} \mathrm{~s}^{-1}\)
Explanation:
$$
\begin{aligned}
&\text { Thrust }=M(g+a)=u \frac{d m}{d t} \\
&\frac{d m}{d t}=\frac{M(g+a)}{u} \\
&=\frac{500(\mathrm{t} 10+20)}{800} \\
&=187.5 \mathrm{~kg} / \mathrm{s}
\end{aligned}
$$

Answer 2

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Answer 3

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