$\"\"$

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The weight of the rocket is $\"\"$ .

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Where $\"\"$ is the surface of the earth and $\"\"$ is the weight of the rocket.

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(a) Find the work is to be done to propel the rocket an unlimited distance away from earths surface.

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The work done by the rocket is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, The work done by the rocket is $\"\"$ .

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$\"\"$

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(b) Find the distance travelled by the rocket when half of the work is done.

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Hence $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The distance travelled by the rocket above the surface of the earth is $\"\"$ .

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$\"\"$

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(a) The work done by the rocket is $\"\"$ .

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(b) The distance travelled by the rocket above the surface of the earth is $\"\"$ .