Question

A particle of mass $2kg$ and charge $0.001C$ is projected vertically with a velocity $10\frac{m}{s}.$ There is a uniform horizontal electric field of ${10}^4\frac{N}{C}$, then which of the following is/are correct? (take $g=10m/s^2$)

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

Answer 1

Answer: (A), (B), (C)

The correct options are
A The horizontal range of the particle is $10m$
B The time of flight of the particle is $2s$
C The maximum height reached is $5m$


The graph will not be a parabola.

$E_x={10}^{4}N{C}^{-1}$
$F_x=q{E}_x={10}^{-3}\times {10}^4=10N$
$a_x=\frac{F_x}{m}=\frac{10}{2}=5m{s}^{-2}$
$a_y=-g$

As body is projected vertically, $u_x=0,u_y=10m{s}^{-1}$
Now using $s=ut+\frac{1}{2}\left(a\right)t^2$, along x and y directions,
$x=\frac{1}{2}\left(5\right)t^2$
$y=10t-\frac{1}{2}\times 10t^2$

Time of flight $T$:
At $t=T,y=0$
$\Rightarrow y=0=10t-5t^2$
$\Rightarrow t=2s$

Range of projectile:
$x=R\text{at}t=2s$
$\Rightarrow R=\frac{1}{2}\times 5\times (2{)}^2$
$=10m$

Maximum Height:
$y=Hatt=1s$
$H=10-5(1{)}^2$
$=5m$