Question

A particle of mass $m$ and charge $q$ is thrown horizontally with a velocity $v$ from top of the building of height $H$. An electric field exists in the plane and it is horizontally away from the building.
Which of the following is true

• A. Range of the particle is greater than $v\sqrt{\frac{2H}{g}}$
• B. Time of flight is $\sqrt{\frac{2H}{g}}$
• C. Path is parabolic
• D. None of the above

Answer 1

Answer: (A)

Range of the particle is greater than $v\sqrt{\frac{2H}{g}}$

Given, u(vertical) = 0 u(hoirzontal)= v

For Time of Flight:

s = ut + $\frac{g{t}^2}{2}$ (applying in vertical direction) (u = 0)

=> H = $\frac{g{t}^2}{2}$

=> t = $\sqrt{\frac{2H}{g}}$

Now, for Range : We know F = ma

=> qE = ma => a = $\frac{qE}{m}$

Now, s (horizontal) = s = ut + $\frac{a{t}^2}{2}$

=> R = v$\sqrt{\frac{2H}{g}}$ +$\frac{qE}{2m}$$\frac{2H}{g}$

which is greater than v$\sqrt{\frac{2H}{g}}$ .