Water level is maintained ina cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel.

Answer

B

Explanation

The velocity with which water will come out
`-:. V=sqrt(2g(H-h))`
`t=(sqrt(2h)/g)`
`=time of flight
`-:.x=vxxt`
`=:.x=vxxt`
`=sqrt(2h(H-h))xxsqrt((2h)/g)`
`=sqrt(4(Hh-h^2))`
for x to be minimum
`d/(dh)(Hh-h^2)=0`
`rarr0=H-2h`
rarr h=H/2`