Q: A water tank stands on the roof of a building as shown. Find the value of h (in m) for which the horizontal
distance ‘x’ covered by the water is greatest.


Ans: 1

Solution: $v_{efflux} = \sqrt{2 g h}$

Time of fall , $t = \sqrt{\frac{2(4-h)}{g}}$

$x = v_{efflux} t = 2\sqrt{h(4-h)}$

the roots of x are (0,4) and the maximum of x is at h = 2. The permitted value of h is 0 to 1 clearly h = 1 will
give the maximum value of x in this interval

Aliter Solution:
If the column of water itself were from ground upto a height of 4m, h = 2m would give the maximum range
x. Farther the hole is from this midpoint, lower the
range. Here the nearest point possible to this midpoint is the base of the container. Hence