Two bodies are thrown with the same initial speed at angles `alpha and (90^(@) -alpha)` with the horizontal. What will be the ratio of (a) maximum heights attained by them and (b) horizontal ranges ?

Explanation

Horizontal range `R=(u^(2))/(g)sin2 theta` and maximum height `H=(u^(2)sin^(2)theta)/(2g)`
Case (i) when `theta=alpha, R_(1)=(u^(2))/(g)sin2alpha` and `H_(1)=(u^(2)sin^(2)alpha)/(2g)`
Case(ii) when `theta=(90^(@)-alpha), R_(2)=(u^(2)sin2(90^(@)-alpha))/(g)=(u^(2)sin(180^(@)-2alpha))/(g)=(u^(2)sin 2alpha)/(g)`
and `H_(2)=(u^(2)sin^(2)(90^(@)-alpha))/(g)=(u^(2)cos^(2)alpha)/(g) (H_(1))/(H_(2))=(sin^(2)alpha)/(cos^(2)alpha)-tan^(2)alpha` and `(R_(1))/(R_(2))=1`