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)`.

Answer

`25`

Explanation

Applying Bernoulli.s theorem just inside (at point (1)) and just outside of the hole (at point (2))
`:.(P_(1))/(rhog)+(v_(1)^(2))/(2g)+y=(P_(2))/(rhog)+(v_(2)^(2))/(2g)+y`
Here `v_(1)=0,P_(2)=P_(0)=` atmospheric pressure
`P_(1)=P_(0)+rhog(H-y)`
`v_(2)=v`
Putting the values we obtain
`1/2rhov^(2)=(H-y)rhog`
`:.v=sqrt(2g(H-y))`
( in horizontal direction)
Horizontal range `I=vt`
For vertical motion
`y=1/2"gt"^(2)`
`:.t=sqrt((2y)/g)`
`:.l=sqrt(2g(H-y))sqrt((2y)/g)`
`=2sqrt(y(H-y))`
For the maximum value of `l,(dl)/(dh)=0`
After solving `y=H/2=25cm`