Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is `pi/3` and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metres is

Options

A. 336
B. 224
C. 56
D. 34

Answer

d

Explanation

For equal range, angles of projection shou ld be `theta` and `(90^(@)-theta)`.
`therefore theta_(!)=(pi)/(3)` and `theta_(2)=(pi)/(2)-(pi)/(3)=(pi)/(6)`
`therefore H_(1)=(u^(2)sin^(2)theta_(1))/(2g)=(u^(2))/(2g)sin^(2)((pi)/(2))=(u^(2))/(2g)((3)/(4))`
and `H_(2)=(u^(2)sin^(2)theta_(2))/(2g)=(u^(2))/(2g)sin^(2)((pi)/(6))=(u^(2))/(2g)((1)/(4))`
`therefore (H_(2))/(H_(1))=(1)/(3), H_(2)=(H_(1))/(3)=(103)/(3)=34m`