The escape velocity for a body of mass $1\, kg$ from the earth's surface is $11.2\, km/s$. The escape velocity for a body of mass $100\, kg$ would be:

Maximum height reached by an object projected perpendicular to the surface of the earth with a speed equal to $50\%$ of the escape velocity from the earth's surface is - ($R =$ Radius of Earth)

The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is:

The masses and radii of the Earth and Moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a body of mass $m$ should be projected from a distance $2d/3$ from the centre of $M_1$ so as to escape to infinity is:

$A$ meteor of mass $m$ having a speed $v$ at infinity reaches the surface of the earth with a speed of (where $v_e$ is the escape speed from the earth's surface).

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)