Determine the hight above the dashed line XX' attained by the water stream coming out through the hole is situtade at point B in the diagram given below. Given that `h=10 m, L=2 m` and `alpha =30^(@)`.

Options

A. 10 m
B. 7.1 m
C. 5 m
D. 3.2 m

Answer

D

Explanation

Let `v_(B)` be the velocity of water coming out from the hole at B. Vertical height of tube of length L at B `=L sin alpha` From law of conservation of total mechanical energy, we have
`mg(h-L sin alpha) =(1)/(2)mv_(B)^(2)`
or `v_(B)^(2) =2 g(h -L sin alpha)`
`=2 g[10-2xx1//2]=18 g`
Let H be the maximum height attained by stream of water coming out of hole, then
`H=L sin alpha +(v_(B)^(2)sin^(2)alpha)/(2g)`
`=2xx1//2+(18 gxx(1//2)^(2))/(2 g) =1+(9)/(4) =3.25 m`