Question

Determine the height above the dashed line $X{X}^{\prime }$ attained by the water stream coming out through the hole is situated at point $B$ in the diagram given below. Given that $h=10m,L=2m$ and $d=30^{\circ }$.

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

Answer 1

Answer: (D)

Let the velocity at point $B$ is $v_B$.
From conservation of total mechanical energy,
$mg[h-L\sin \alpha ]=\frac{1}{2}m{v}_B^2$
$\Rightarrow v_B^2=2g(h-L\sin \alpha )$
$=2g\left(10-2\times \frac{1}{2}\right)$
$\Rightarrow v_B^2=18g$
Now, let maximum height attained by water stream, be $(H)$.
$\therefore H=L\sin \theta +\frac{V_B^2{\sin }^2\alpha }{2g}$
$\Rightarrow H=2\times \frac{1}{2}+\frac{18g{\left(\frac{1}{2}\right)}^2}{2g}$
$=1+\frac{18}{8}=3.25m$