Water level is maintained in a cylindrical vessel upto 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 of the greatest distance from the vessel?

Step-by-step solution

The velocity with which water will came out v= 2 g(H-h) The time of flight of water ejected from the hole. aligned t & = 2 h g = time of flight x & =v t & = 2 g(H-h) 2 h g = 4 (H h-h^2 ) aligned For x to be maximum aligned & d x d h =0 & d 4 (H h-h^2 ) d h =0 & 0=H-2 h h= H 2 aligned