If the angle of projection of a projector with same initial velocity exceed or fall short of `45^(@)` by equal amount `alpha`, then the ratio of horizontal rages is

Options

A. `1 :2`
B. `1:sqrt2`
C. `1:4`
D. `1:1`

Answer

D

Explanation

Let u be the initial velocity of the projectile .
For angle of projection `(45^(@) + alpha)` horizontal range is
`R_(1) = (u^2 sin (45^(@)) + alpha )/g =(u^(2) sin (90^(@) + 2alpha))/g =(u^2 cos 2 alpha)/g`

For angle of projection `(45^(@) - alpha)` horizontal range is
`R_(2) = (u^2 sin (45^(@)) - alpha )/g =(u^(2) sin (90^(@) - 2alpha))/g =(u^2 cos 2 alpha)/g`
`:. R_1/R_2=1`