Question

A wide cylindrical vessel $50cm$ in height is filled with water and rests on a table. Assuming the viscosity to be negligible, find at what height from the bottom of the vessel a small hole should be perforated for the water jet coming out of it to hit the surface of the table at the maximum distance $l_{max}$ from the vessel.

• A. $h=25cm$
• B. $h=50cm$
  
• C. $h=65cm$
  
• D. $h=75cm$
  

Answer 1

The correct option is A $h=25cm$

$Letxbetheheightfromthebottomvelocityofefflux=\sqrt{2g(H-x)}$

$Timetakentoreachbottom=\sqrt{\frac{2x}{g}}$

$horizontaldisplacementofwater=vt=\sqrt{2g(H-x)}\times \sqrt{\frac{2x}{g}}$

$s=2\sqrt{x(H-x)}$

$tomaximizesdifferentiateandequateto0$

$\frac{ds}{dx}=\frac{2}{2\sqrt{x(H-x)}}(H-2x)=0\Rightarrow x=\frac{H}{2}=\frac{50cm}{2}=25cm$

Hence option ${}^{\prime }{A}^{\prime }$ is the answer.