Question

The escape velocity of a projectile on the earth's surface is $11.2km{s}^{-1}$. A body is projected out with thrice this speed. Then, the speed of the body far from the earth, ignoring the presence of the sun and other planets will be

• A. $11.2km{s}^{-1}$
• B. $22.4km{s}^{-1}$
• C. $31.7km{s}^{-1}$
• D. $11.4km{s}^{-1}$

Answer 1

The correct option is C $31.7km{s}^{-1}$

Escape velocity $v_e={\left(\frac{2GM}{R}\right)}^{0.5}\to \frac{(v_e{)}^2}{2}=\frac{GM}{R}$

if it is given thrice the speed $V=3v_e$

Now by conservation of energy, $\frac{-GMm}{R}+\frac{m{V}^2}{2}=0+\frac{m{v}^2}{2}$

$\frac{-m{v_e}^2}{2}+\frac{m(3v_e{)}^2}{2}=\frac{m{v}^2}{2}$

By solving the above equation$,v=8^{0.5}{v}_e=8^{0.5}\left(11.2\right)=31.7km{s}^{-1}$