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Physics / College Physics 1 / Chapter 8 / Problem 60

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

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Solved: How much of a single-stage rocket that is 100,000

Chapter 8, Problem 60

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QUESTION:

Problem 60PE

How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of 8.00 km/s , given that it expels gases at an exhaust velocity of 2.20×103 m/s?

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QUESTION:

Problem 60PE

How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of 8.00 km/s , given that it expels gases at an exhaust velocity of 2.20×103 m/s?

ANSWER:

Solution 60PE

Step 1 of 3

For the given single stage rocket with rest mass ${m}_{0}=100,000\ kg$ , we need to calculate the final mass of the rocket after firing ${m}_{r}=?$ and attaining a final speed of ${v}_{f}=8\ km/s$ with the exhaust velocity of expels gases at ${v}_{e}=2.2\times{}{10}^{3}m/s$ .

Given data,

Rest mass of rocket, ${{m}_{0}=100,000\ kg}_{\ }$

Using ${100,000kg=10}^{5}kg$ ${{m}_{0}={10}^{5}\ kg}_{\ }$

Final velocity of rocket, ${v}_{f}=8\ km/s$

Using ${8\ km=8\times{}10}^{3}m$ ${v}_{f}={8\times{}10}^{3}m/s$

Exhaust velocity of expel gases, ${v}_{e}=2.2\times{}{10}^{3}m/s$

To find,

Final mass of rocket after firing, ${m}_{r}=?$

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