A uniform electric field,  $\overrightarrow{E}=-400\sqrt{3}\widehat{y}N{C}^{-1}$  is applied  in a region . A charged particle of mass m carrying positive charge q is projected in this region with an initial speed  of  $2\sqrt{10}\times {10}^{6}m{s}^{-1}$ . This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as  shown schematically in the figure . $Take\frac{q}{m}={10}^{10}Ck{g}^{-1}$. Then 

Given: electric field , ${\overrightarrow{E}}_y=-400\sqrt{3}N{C}^{-1}$  Initial speed of charged particle, $u=2\sqrt{10}\times {10}^{6}m/s$   Range , R=5m    
 $F=maandF=qE\therefore a_y=\frac{q}{m}{E}_y=-400\sqrt{3}\times {10}^{10}$
 $[\therefore \frac{q}{m}={10}^{10}Ck{g}^{-1}\left(given\right)]$
 $Range,R=\frac{u^2\sin 2\theta }{a_y}\Rightarrow 5=\frac{40\times {10}^{12}\sin 2\theta }{400\sqrt{3}\times {10}^{10}}$  $\Rightarrow \sin 2\theta =\frac{\sqrt{3}}{2}$

$\Rightarrow 2\theta ={60}^{0}or,120\Rightarrow \theta ={30}^{0}or,{60}^0$
 Particle hits the target, if  $\theta ={30}^{0}or\theta ={60}^0$
  $u=2\sqrt{10}\times {10}^{6}m{s}^{-1}$

  
Time of flight  $T_1=\frac{2u\sin \theta }{a_y}=\frac{2\times 2\sqrt{10}\times {10}^6\times \frac{1}{2}}{400\sqrt{3}\times {10}^{10}}$   $=\sqrt{\frac{5}{6}}\mu s(for\theta ={30}^0)$
 
Time of flight  $T_2=\frac{2u\sin \theta }{a_y}=\frac{2\times 2\sqrt{10}\times {10}^6\times \frac{\sqrt{3}}{2}}{400\sqrt{3}\times {10}^{10}}$$=\sqrt{\frac{5}{6}}\mu s(for\theta ={60}^0)$