$\"\"$

(a).

The equation is $\"\"$ .

Where $\"\"$ is velocity.

$\"\"$ is accleration due to garvity.

$\"\"$ is maximum height reached.

Accleration due to gravity is $\"\"$ .

Substiute $\"\"$ in $\"\"$ .

$\"\"$

Squaring on both sides.

$\"\"$

The equation that will give maximum height of water as a function as its velocity is $\"\"$ .

$\"\"$

(b).

Velocity $\"\"$ \ \

Substiute $\"\"$ in the obtained equation $\"\"$ .

$\"\"$

The pump can propel water to a height of about $\"\"$ . \ \

$\"\"$

(a). \ \

The equation that will give maximum height of water as a function as its velocity is $\"\"$ .

(b). \ \

The pump can propel water to a height of about $\"\"$ . \ \

So the pump will meet the fire department needs. \ \