The escape velocity of a body on the earth surface is 11.2 km/s. If the same body is projected upward with velocity 22.4 km/s, the velocity of this body at infinite distance from the centre of the earth will be:

If a body is projected with escape velocity, it reaches infinity with zero energy as all its energy is used to overcome the gravitational pull. If it is projected with a velocity more than escape velocity, then even after reaching infinity, it has some kinetic energy. From conservation of energy,

$\frac{1}{2}m{v}_0^2-\frac{GMm}{R}=\frac{1}{2}m{v}^2\dots \text{(i)}$

where m and M are the mass of the body and the planet, respectively.

$-\frac{\mathrm{GMm}}{\mathrm{R}}$ is the potential energy at the surface of the earth, v₀ is the velocity of projection, v is the velocity at infinity. From the concept of escape velocity,

$\frac{\mathrm{GMm}}{\mathrm{R}}=\frac{1}{2}{{\mathrm{mv}}_{\mathrm{e}}}^2$

Then equation i becomes

$\frac{1}{2}m{v}_0^2-\frac{1}{2}m{v}_e^2=\frac{1}{2}m{v}^2$

$v=\sqrt{v_0^2-{v_e}^2}=\sqrt{(22.4{)}^2-(11.2{)}^2}$

$=11.2\sqrt{3}\mathrm{km}/\mathrm{s}\text{.}$