Question

A charged particle of mass $m=2\, kg$ and charge $1\, \mu C$ is thrown from a horizontal ground at an angle of $45^{\circ}$ with horizontal with a speed of $10\, m / s$. 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)

$a_{x}=\frac{q E}{m}=\frac{10^{-6} \times 2 \times 10^{7}}{2}=10 \,m / s ^{2}$

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