8.17 A rocket is fired vertically with a speed of 5 km s-1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth = 6.0 × 1024 kg; mean radius of the earth = 6.4 × 106 m; G = 6.67 × 10–11 N m2 kg–2.
8.17 A rocket is fired vertically with a speed of 5 km s-1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth = 6.0 × 1024 kg; mean radius of the earth = 6.4 × 106 m; G = 6.67 × 10–11 N m2 kg–2.
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1 Answer
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Velocity of the rocket, v = 5 km/s = 5 m/s
Mass of the Earth, = 6.0 * 1024 kg
Radius of the Earth, = 6.4 * 106 m
Height reached by rocket mass, m = h
At the Earth's surface
Total energy of the rocket = Kinetic energy + Potential energy = m + ( )
At highest point h, v = 0, and potential energy =
Total energy of the rocket at height h =
From the law of conservation of energy, we have,
Total energy of the rocket at Earth surface = Total energy at height h
m + ( ) = or =
= = = =
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