Question

A charged particle of mass $m=2kg$ and charge $1\mu C$ is thrown from a horizontal ground at an angle of $45^{\circ }$ with horizontal with a speed of $10m/s$. In space a horizontal electric field $E=2\times 10^{7}N/C$ exists. Find the range of the projectile.

• A. 5 m
• B. 30 m
• C. 10 m
• D. 20 m

Answer 1

Answer: (D)

$a_x=\frac{qE}{m}=\frac{10^{-6}\times 2\times 10^7}{2}=10m/s^2$

Time of flight, $T=\frac{2u\sin \theta }{g}=\frac{2\times 10\times \frac{1}{\sqrt{2}}}{10}=\sqrt{2}s$
Hence, range, $R=u_{x}T+\frac{1}{2}{a}_x{T}^2$
$R=10\cos 45^{\circ }\times T+\frac{1}{2}{a}_x{T}^2$
$=\frac{10}{\sqrt{2}}\times \sqrt{2}+\frac{1}{2}\times 10\times 2=20m$