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 sin 2 theta`
and maximum height, `H = (u^(2) sin^(2)theta)/(2g)`
When `theta=alpha,R_(1)=u^2/gsin2alpha and H_(1)=(u^(2) sin ^(2) alpha)/(2g)`
When `theta = (90^(@) - alpha)`,
`R_(2) = (u^(2) sin (90^(@) - alpha))/g = (u^(2) sin (180^(@) - 2alpha))/g=(u^2 sin 2alpha )/g`
and `H_(2)=(u^2 sin^(2)(90^(@) - alpha))/(2g)=(u^2cos^(2) alpha)/(2g)`
`:. H_1/H_2=(sin^(2) alpha)/(cos^2alpha)= tan^(2) alpha andR_1/R_2=1`