Ratio of the ranges of the bullets fired from a gun `(` of constant muzzle speed `)` at angle `theta, 2 theta &4 theta` is found in the ratio `x:2:2`, then the value of `x` will be `(` Assume same muzzle speed of bullets `)`

Options

A. `1`
B. `2`
C. `sqrt(3)`
D. `2/(sqrt(3))`

Answer

D

Explanation

Range is same for `2 theta` and `4 theta`
`:. 2 theta + 4 theta = 90^(@) rArr theta = 15^(@)`
`:.` Range of ranges will be
`sin 30^(@) : sin 60^(@) : sin 120^(@)`.