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. 3.36
B. 224
C. 56
D. 34

Answer

D

Explanation

Horizontal ranges are same for comple mentary angles of projection, ie, for `theta and (90^(@)-theta)`
We know that iftwo stones have same horizontal range, then this implies that both are projected at `theta and (90^(-@)-theta)`
Here, `theta=(pi)/(3)=60^(@)`
`:.90^(@)- theta=90^(@)-60^(@)=30^(@)`
for first stone :
Max height `=102=(u^(2) sin^(2) 60^(2))/(2g)`
For second stone
Max height `=(u^(2) sin^(2) 30^(2))/(2g)`
`:.(h)/(102)=(sin^(2)30^(@))/(sin^(2)60^(@))`
`=((1//2)^(2))/((sqrt(3)//2)^(2))`
or `h=102xx(1//4)/(3//4)=34 m`