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. Find `l_(max)`.

Explanation

Let, H be the total height of water column and the hole is made at a height h from the bottom.
Then from Bernoulli's theorem
`1/2rhov^2=(H-h)rhog`
or, `v=sqrt((H-h)2g)`, which is directed horizontally.
For the horizontal range, `l=vt`
`=sqrt(2g(H-h))*sqrt((2h)/(g))=2sqrt((Hh-h^2))`

Now, for maximum `l`, `(d(Hh-h^2))/(dh)=0`
which yields `h=H/2=25cm`.