Question
A rocket is fired vertically with a speed of 5 km/s from the earth’s surface. How far from the earth’s surface does the rocket go before returning to the earth? Mass of the earth = 6.0 x 1024 kg; mean radius of the earth = 6.4 x 106 m; G =6.67 x 10-11 N m2 kg-2.
Acceleration due to gravity at the surface of the earth = 9.8 m/s2.
Solution
When a body is thrown a body in the upward direction, the kinetic energy of the body converts into potential energy.
Potential energy of the body at ground is,
If the body is raised to a height h from the earth, then potential energy at height h is,
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Therefore increase in potential energy is,
The increase in potential energy is at the cost of kinetic energy, therefore
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Here, we have
Therefore,
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That is, the rocket travels a distance of 1.6 x 106 m before returning to the Earth's surface.
Potential energy of the body at ground is,
If the body is raised to a height h from the earth, then potential energy at height h is,
Therefore increase in potential energy is,
The increase in potential energy is at the cost of kinetic energy, therefore
Here, we have
Therefore,
That is, the rocket travels a distance of 1.6 x 106 m before returning to the Earth's surface.
