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From the data in .7 you can find the space shuttle's
Chapter 3, Problem 3.9(choose chapter or problem)
From the data in Problem 3.7 you can find the space shuttle's initial mass and the rate of ejecting mass \(-\dot{m}\) (which you may assume is constant). What is the minimum exhaust speed \(v_{\mathrm{ex}}\) for which the shuttle would just begin to lift as soon as burn is fully underway? [Hint: The thrust must at least balance the shuttle's weight.]
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QUESTION:
From the data in Problem 3.7 you can find the space shuttle's initial mass and the rate of ejecting mass \(-\dot{m}\) (which you may assume is constant). What is the minimum exhaust speed \(v_{\mathrm{ex}}\) for which the shuttle would just begin to lift as soon as burn is fully underway? [Hint: The thrust must at least balance the shuttle's weight.]
ANSWER:Step 1 of 2
The maximum exhaust speed is the speed of exhaust required to just start the rocket. In this case, the weight of the rocket is balanced by thrust.
\(\begin{array}{l}
m g=-m v_{\text {ex }} \\
v_{\text {ex }}=\frac{m g}{-m}
\end{array}\)
Find the mass \(\dot m\) as follows.
\(\begin{aligned}
\dot m & =\frac{\left(1 \times 10^{6} \mathrm{~kg}\right)-\left(2 \times 10^{6} \mathrm{~kg}\right)}{(2 \mathrm{~min})\left(\frac{60 \mathrm{~s}}{1 \mathrm{~min}}\right)} \\
& =-8333 \mathrm{~kg} / \mathrm{s}
\end{aligned}\)
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