let hole be made at height 'h' from the ground

so, pressure at the level wher hole is made is given by

P = (H-h)g

and F= PA = (H-h)gA

acceleration of water = a = F/m = (H-h)gA/m

Now, time taken by the stream to fall on the ground from height 'h' is

t = 2gh

Therefore, Horizontal distance travelled in time 't' is

x = ut + (1/2)at²

or, x = (1/2) [ (H-h)gA/m] [2gh]

or, x = (H-h)g²Ah/m

so, for x = maximum

dx/dh = 0

dx/dh = -g²Ah/m +(H-h)g²A/m

or (H-h)g²A/m = g²Ah/m

or (H-h) = h

or h = H/2 is the reqiured solution