a tankis filled up to aheight 2H WITH A LIQUID and is placed on a platform of height H from theground .the distance x from the ground where a small hole is punched toget maximum range R is?

(squareroot of 24)H

The pressure of liquid is maximum at the bottom of the liquid in the tank.

So to get the maximum range, the hole must be pierced at the bottom of the tank, i.e., 

the required  height x must be equal to H.

with regards, 

Rishabh class xii

the value of x= 3h/2

since v=√2gh   and in questiion h=3h-x

and range r=vt (projectile)

so    r= [√2g(3h-x)][√2x/g]

simplifying

we have r is maximum if (3h-x).x is maximum

which is maximum at x=3h/2

its the same question asked just before.

ans is x=3H/2.

3H/2

let x be the distance fom the grond then here we have a horizontal projectlie time to come to grond =1/2 gt^2=x forwrd velocity =sqrt(2g(3h-x)) range=time *velocity; range =3h/2 (we would get a function for range which can be maximised using maxima and minima dr/dx=0 )