prove that a gun will shoot three times as high when its angle of elevation 60 degree as when it is 30 degree, but cover the same horizontal range.

We know that Maximum height reached, H =

and, horizontal range R = '

For θ = 30⁰,

 

H₁ = = =

R₁ = =

 

For θ = 60⁰ ,

 

H₂ = =

R₂ = =

Therefore,

 

Hence Proved.