Choose the correct alternative.

A rocket is fired vertically with a speed of \(5\) km/s from the earth’s surface. How far from the earth does the rocket go before returning to the earth?
1. \(8\times10^6\) m
2. \(1.6\times10^6\) m
3. \(6.4\times10^6\) m
4. \(12\times10^6\) m

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×${10}^8$ km; G = 6.67×${10}^{-11}$$N<mspace\; width="1em"></mspace>m^2<mspace\; width="1em"></mspace>k{g}^{-2}$.)
1. 11 × 10¹⁰ J
2. 6 × 10¹¹ J
3. 6.67 × 10¹⁰ J
4. 7.12 × 10¹¹ J

A rocket is fired vertically from the surface of mars with a speed of 2 km/s. 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×${10}^{23}$ kg; radius of mars = 3395 km; G = 6.67×${10}^{-11}$ $N<mspace\; width="1em"></mspace>m^2<mspace\; width="1em"></mspace>k{g}^{-2}.$)

1. 477.2 km
2. 550.5 km
3. 493.9 km
4. 517.3 km