How do you approach Problem 14-71?

To find $x$, the distance at which the stream hits the ground, you need to find the velocity $v$ with which the stream comes out of the hole; if you have this, you can just use 1D kinematics. Now to find $v$, use Bernouilli, realizing that the pressure is atmospheric where the water is in contact with the air.

For part $b$, use your expression for $x$ in terms of $H$ and $h$ to solve for possible values of $h$, given $x$ and $H$.

For part $c$, find the value of $h$ that maximizes $x=f(h)$.