Two stones are projected with the same speed but making different angles with the horizontal. Their reanges are equal. If the angles of projection of one is `pi//3` and its maximum height is `h_(1)` then the maximum height of the other will be:

Options

A. `3y_(1)`
B. `2y_(1)`
C. `(y_(1))/(2)`
D. `(y_(1))/(3)`

Answer

D

Explanation

For same range `theta_(1)+theta_(2)=90^(@)`
`theta_(1)=(pi)/(3)rad=60^(@)`
`therefore theta_(2)=90^(@)=30^(@)`
`y_(1)=(u^(2)sin^(2)60^(@))/(2g)=(u^(2)xx3)/(2gxx4)rArr(u^(2))/(8g)=(y_(1))/(3)`
`y_(2)=(u^(2)sin^(2)30^(@))/(2g)=(u^(2)xx1)/(2gxx4)=(y_(1))/(3)`