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A rocket (initial mass m0) needs to use its engines to
Chapter 3, Problem 3.8(choose chapter or problem)
A rocket (initial mass \(m_{\mathrm{o}}\)) needs to use its engines to hover stationary, just above the ground.
(a) If it can afford to burn no more than a mass \(\lambda m_{0}\) of its fuel, for how long can it hover? [Hint: Write down the condition that the thrust just balance the force of gravity. You can integrate the resulting equation by separating the variables t and m. Take \(v_{\text {ex }}\) to be constant.]
(b) If \(v_{\mathrm{ex}} \approx 3000 \mathrm{~m} / \mathrm{s}\) and \(\lambda \approx 10 \%\), for how long could the rocket hover just above the earth's surface?
Questions & Answers
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QUESTION:
A rocket (initial mass \(m_{\mathrm{o}}\)) needs to use its engines to hover stationary, just above the ground.
(a) If it can afford to burn no more than a mass \(\lambda m_{0}\) of its fuel, for how long can it hover? [Hint: Write down the condition that the thrust just balance the force of gravity. You can integrate the resulting equation by separating the variables t and m. Take \(v_{\text {ex }}\) to be constant.]
(b) If \(v_{\mathrm{ex}} \approx 3000 \mathrm{~m} / \mathrm{s}\) and \(\lambda \approx 10 \%\), for how long could the rocket hover just above the earth's surface?
ANSWER:
Step 1 of 3
(a)
The thrust is given by, \(\mathrm{F}=\mathrm{v}_{\mathrm{ex}} \frac{\mathrm{dm}}{\mathrm{dt}}\).
Where \(v_{e x}\) is the exhaust velocity.
Then we can write, \(-m g=m v_{a}\), as the mass is decreasing.
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Review this written solution for 101252) viewed: 698 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 3 - Problem 3.8
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