Galileo writes that for angles of projection of a projectile at angles `(45 + theta)` and `(45 - theta)`, the horizontal ranges described by the projectile are in the ratio of (if `theta le 45`)

Options

A. `2:1`
B. `1:2`
C. `1:1`
D. `2:3`

Answer

C

Explanation

For angle `(45^(@) - theta), R_(1) = (u^(2) sin(90 - 2theta))/g = (u^(2) cos 2theta)/g`…….. (i)
For angle `(45^(@) + theta), R_(2) = (u^(2) sin (90 + 2theta))/g = (u^(2) cos 2theta)/g`…… (ii)
By eq. (i) & (ii), `R_(2)/R_(1) 1:1`