# A particle is fired upward with a speed of $20 \;Km/s$. The speed with which it will move in in interstellar space is

$(a)\;8.8 km/s \quad (b)\;16.5\; km/s \quad (c)\;11.2\;km/s \quad (d)\;10\;km/s$

From conservation of energy
$\large\frac{1}{2} $$mv^2 =\large\frac{1}{2}$$m [(20)^2 -v_e^2]$
$v_e$ -escape velocity
$\qquad= 8 \sqrt 2 km/s$
$v^2=20^{2}-(8\sqrt 2)^2$
$v=16.5 km/s$
Hence b is the correct answer.

edited Feb 18, 2014 by meena.p