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If the angle of projection of a projecto...

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

A

`1:2`

B

`1:3`

C

`1:4`

D

`1:1`

Text Solution

Verified by Experts

The correct Answer is:
D
let u be 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))/()=(u^(2)cos 2alpha)/(g)`
For angle ofprojection `(45^(2)+alpha)` horizontal range is
`R_(2)=(u^(2)sin2(45^(@)-alpha))/(g)=(u^(2)sin(90^(@)-2alpha))/()=(u^(2)cos 2alpha)/(g)`
`:.(R_(1))/(R_(2))=1`
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