Question

The escape velocity of a body from earth is $11.2km/s$. If a body is projected with a velocity twice its escape velocity, then the velocity of the body at infinity is :

• A. $19.4km/s$
• B. $194km/s$
• C. $1.94km/s$
• D. $0.194km/s$

Answer 1

Answer: (A)

$19.4km/s$

Using energy conservation principle
$P.E{.}_i+K.E_i=P.E{.}_f+K.E_f$
where subscripts i and f for initial and final potential and kinetic energy of body
$-\frac{GMm}{r}+\frac{1}{2}m(2v_e{)}^2=0+\frac{1}{2}m{v^{\prime }}^2$...$\left(i\right)$

$v_e=\sqrt{2GM}R\Rightarrow \frac{GM}{R}=\frac{{v_e}^2}{2}$...$\left(ii\right)$
substituting relation in equation $\left(i\right)$

$-m\frac{1}{2}{v_e}^2+\frac{1}{2}m(2v_e{)}^2=\frac{1}{2}m{v^{\prime }}^2$

Solving for $v^{\prime }=\sqrt{3}{v}_e=19.4km/s$