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

The escape speed of a projectile on the earth’s surface is 11.2 km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth?  (Ignore the presence of the sun and other planets.)

1. 32.7 km/s

2. 11.2 km/s

3. 31.7 km/s

4. 21.2 km/s

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 m^2 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×${10}^{-11}$ $N m^2 k{g}^{-2}.$)

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