Prove that the horizontal range is same when angle of projection is(i)

1.	Prove that the horizontal range is same when angle of projection is(i) greater than 45° by certain value, and(ii) less than 45° by the same value.
Answer» (i) When the angle of projection, θ = 45^o + α , the horizontal range is \(R=\frac{u^2\,sin\,2\,(45^0+\alpha)}{g}\) = \(\frac{u^2sin(90^0+2\alpha)}{g}\) = \(\frac{u^2\,cos\,2\alpha}{g}\) (ii) When the angle of projection, θ = 45^o – α, the horizontal range is Clearly, R' = R

Prove that the horizontal range is same when angle of projection is(i) greater than 45° by certain value, and(ii) less than 45° by the same value.

Answer»

(i) When the angle of projection, θ = 45^o + α , the horizontal range is

\(R=\frac{u^2\,sin\,2\,(45^0+\alpha)}{g}\)

= \(\frac{u^2sin(90^0+2\alpha)}{g}\)

= \(\frac{u^2\,cos\,2\alpha}{g}\)

(ii) When the angle of projection, θ = 45^o – α, the horizontal range is

Clearly, R' = R