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#### Question

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 × 10^{24} kg; mean radius of the earth = 6.4 × 10^{6} m; G= 6.67 × 10^{–11} N m^{2} kg^{–}^{2}

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Choose the correct alternative:

The formula –*G Mm*(1/*r*_{2}– 1/*r*_{1}) is more/less accurate than the formula *mg*(*r*_{2}– *r*_{1}) for the difference of potential energy between two points *r*_{2}and *r*_{1}distance away from the centre of the earth.

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the Sun = 2 × 10^{30} kg; mass of mars = 6.4 × 10^{23} kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 × 10^{8}kg; G= 6.67 × 10^{–11} m^{2}kg^{–2}.

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4× 1023 kg; radius of mars = 3395 km; G = 6.67× 10^{-11} N m^{2} kg^{–2}.