A particle of mass ma and charge q has been projected from ground as shown in fig. Mark the correct statement(s) (xy) plane is vertical.

Options

A. The path of motion of the particle may be parabolic.
B. The pathof motion of the particle may be a straight line.
C. Time of flight of the particle is `2u sin theta//g`
D. Range of motion of the particle can be less than, greater than, or equal to `u^(2)sin 2 theta//g`.

Answer

A, B, C

Explanation

Along x-axis `u_(x)=u cos theta implies a_(x)=-(qE)/(m)`
Along y-axis `u_(x)=u sin theta implies a_(y)=-g`
Equation of motion along x- and y- axes would beas follows: a is resultant acceleration. If a is opposite to u, i.e. `alpha=theta` then the path will be a straight line. For `a!=theta` the path will be parabolic. Will be a parabolic. Time of flight remains unchanged as vertical motion is not affected by `vec(E )`. Range of the particle in the present case is always less than `u^(2) sin 2 theta//g` whatever may be the value of E.
`R=x_(t)=u cos theta xx(2u sin theta)/(g)-1/2`
`xx(qE)/(m)[(2u sin theta)/(g)]^(2)lt(u^(2)sin 2 theta)/(g)`.