The escape velocity of a projectile on the surface of earth is $11.2 km/s$. If a body is projected out with thrice of this speed, find the speed of the body far away from the earth.
Ignore the presence of other planets and sun.

$v_e = 11.2 km/s$, velocity of projection $= v = 3v_e$
Let $m$ and $v_o$ be the mass and the velocity of the projectile far away from the earth, then using law of conservation of energy,

         $$\begin{gathered} \frac{1}{2}m{v}_0^2 = \frac{1}{2}m{v}^2-\frac{1}{2}m{v}_e^2 \\ {v}_0 = \sqrt{v^2-v_e^2 } = \sqrt{{\left(3v_e\right)}^2-v_{{ }_e}^2} = \sqrt{8} v_e \\ = 2\sqrt{2}\times 11.2 = 2\times 1.414\times 11.2 = 31.68 km/s \end{gathered}$$