For angles of projection of a projectile at angle `(45^(@) - theta) and (45^(@)+ theta)`, the horizontal ranges described by the projectile are in the ratio of :

Options

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

Answer

C

Explanation

For a projectile launched with velocity u at an angle `theta`, the horizontal range is given by
`R=(u^(2)sin 2 theta)/g`
(i) for `theta_(1)=45^(@)- theta`
`R_(1)=(u^(2)sin (90^(@)-2 theta))/g=(u^(2)cos 2 theta)/g`
(ii) For `theta_(2)=45^(@)+ theta`