Question

The escape velocity from earth is $v_e$. A body is projected with velocity $2v_e$. With what constant velocity will it move in the inter planetary space?

• A. $v_e$
• B. $\sqrt{2}{v}_e$
• C. $\sqrt{3}{v}_e$
• D. $\sqrt{5}{v}_e$

Answer 1

The correct option is C $\sqrt{3}{v}_e$

$U_i+K_i=U_f+K_f$
$-\frac{GMm}{R}+\frac{1}{2}m(2V_e{)}^2=0+\frac{1}{2}m{v}^2$
or $-\frac{GM}{R}+2v_e^2=\frac{1}{2}{v}^2$
or $-\frac{2GM}{R}+\frac{8GM}{R}=v^2$
$v=\sqrt{\frac{6GM}{R}}=\sqrt{3\left(\frac{2GM}{R}\right)}$
$=\sqrt{3\left(2gR\right)}=\sqrt{3}{V}_e$