# A charged particle of mass $\;m= 1 kg\;$ and charge $\;q=2\;\mu C\;$ is thrown from a horizontal ground at an angle $\;\theta=45^{0}\;$ with speed $\;20\;m/s\;.$ In space a horizontal electric field $E=2\times10^{6}\;V/m\;$ exist Find the range on horizontal ground of the projectile

$(a)\;200m\qquad(b)\;164 m\qquad(c)\;56 m\qquad(d)\;40 m$

Explanation :
The path of the particle will be a parabola , but along x - axis also motion of the particle will be accelerated . Time of flight of particle is
$T=\large\frac{2u_{y}}{g}=\large\frac{2\times20 cos 45^{0}}{10}=2 \sqrt{2} s$
Horizontal range R = $\;u_{x} T + \large\frac{1}{2} a_{x} T^{2}$
$a_{x}=\large\frac{qE}{m}=\large\frac{2\times2\times10^{-6}\times10^{6}}{1}$
$=4 m/s^{2}$
$R=(20 \large\frac{1}{\sqrt{2}})\;(2 \sqrt{2})+\large\frac{1}{2}\times4\times8$
$=40+16$
$=56 m$
edited Feb 20, 2014 by yamini.v