Question

A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity $10m{s}^{-1}$. There is a uniform horizontal electric field of ${10}^4$ N/C :

• A. The horizontal range of the particle is 10 m
• B. The time of flight of the particle is 2 s
• C. The time of flight of the particle is 5 s
• D. The horizontal range of the particle is 5 m
  

Answer 1

Answer: (A), (B)

The correct options are
A The time of flight of the particle is 2 s
B The horizontal range of the particle is 10 m

Given : $q={10}^{-3}$ C $m=2kg$ $u_y=10$ m/s $E={10}^4$ N/C $u_x=0$ m/s $a_y=-10$ $m/s^2$

Let time of flight be $T$ and horizontal range be $S_x$.

Vertical direction :

Using $S_y=u_{y}t+\frac{1}{2}{a}_y{t}^2$ where $S=0$ @ $t=T$

$\therefore$ $0=10T-\frac{1}{2}\left(10\right)T^2$ $⟹T=2$ s

Horizontal direction :

Horizontal acceleration $a_x=\frac{qE}{m}=\frac{{10}^{-3}\times {10}^4}{2}=5$ $m/s^2$

Horizontal range, $S_x=u_{x}T+\frac{1}{2}{a}_x{T}^2$

$\therefore$$S_x=0+\frac{1}{2}\left(5\right)(2{)}^2=10$ m