$A$ spaceship moves from the Earth to the Moon and back. The greatest energy required for the spaceship is to overcome the difficulty in:

The escape velocity for a rocket from Earth is $11.2 \ km/s$. Its value on a planet where the acceleration due to gravity is double that on the Earth and the diameter of the planet is twice that of Earth will be in $km/s$:

$A$ body of mass $m$ is situated at a distance $4R_e$ above the Earth's surface,where $R_e$ is the radius of Earth. How much minimum energy must be given to the body so that it may escape?

$A$ small asteroid is orbiting around the sun in a circular orbit of radius $r_0$ with speed $v_0$. $A$ rocket is launched from the asteroid with speed $v = \alpha v_0$,where $v$ is the speed relative to the sun. The highest value of $\alpha$ for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets).

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 (in $km/s$) of the body far away from the earth? Ignore the presence of the sun and other planets.

$A$ body is projected vertically upwards from the surface of the Earth with a velocity equal to one-third of the escape velocity. The maximum height attained by the body will be $...... \ km$. (Take radius of Earth $R = 6400 \ km$ and $g = 10 \ m/s^2$)