A uniform electric field `vec(e )=-4000sqrt(3)hat(y)NC^(-1)` is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speen of `2sqrt(10)xx10^(6)ms^(-1)`. This particle is aimed to hit a target T, which is 5 m away from its entry point the field as shown schematically in the figure.
Take `(q)/(m)=10^(10)Ckg^(-1)`, Then

Options

A. the particle will hit T if projected at an angle `45^(@)` from the horizontal
B. the particle will hit T if projected at an angle `45^@` from horizontal
C. time taken by the particle to hit T could be `sqrt((5)/(6))mus` well as `sqrt((5)/(2))mu m`
D. time taken by the particle to hit T is `sqrt((5)/(3))mu s`.

Answer

C

Explanation

`a_(y)=(e )/(M)=4sqrt(3)xx10^(12)m//s^(2)`

`R=(u^(2)sin2theta)/(a_(y))`
`sin2theta=(Ra_(y))/(u^(2))=(sqrt(3))/(2)`
`theta=30^(º)` or `60^(º)`
`T=(2usin30^(º))/(a_(y))` or `(2usin60^(º))/(a_(y))`
`=sqrt((5)/(6))mu s` or `sqrt((5)/(2))mu s`.