A projectile aimed at a mark, which is in the horizontal plane through the point of projection, falls a cm short of it when the elevation is `alpha` and goes b cm far when the elevation is `beta`. Show that, if the speed of projection is same in all the cases the proper elevation is
`1/2 sin^(-1) [(bsin2alpha+asin2beta)/(a+b)]` .

Answer

A

Explanation

`R - a = (u^2 sin 2 alpha)/g`
Multiplying with b we have,
`bR - ab = (bu^2 sin 2alpha)/g`………..(i)
`R + b = (u^2sin2beta)/g`
Multiplying with a we have,
`aR + ab = (au^2sin 2beta)/g` ……..(ii)
Adding Eqs. (i) and (ii) and by putting
`R = (u^2sin 2theta)/g,`
we get the result.