If a fire hose is held horizontally, then the distance the stream will travel depends on the water pressure and on the horizontal factor for the nozzle. The horizontal factor H depends on the diameter of the nozzle. For a 0.5-inch nozzle, the horizontal factor is 56. For each 1/8-inch increase in nozzle diameter, the horizontal factor increases by 6.
(a) Explain why the function giving the horizontal factor H in terms of the nozzle diameter d (measured in inches) is linear.
(Because the horizontal factor H always increases by 6, when d increases by 1/8, the horizontal factor has a constant rate of change.)
(b) Use a formula to express H as a linear function of d.
(c) Once the horizontal factor H is known, we can calculate the distance S in feet that a horizontal stream of water can travel by using the following formula where p is pressure in pounds per square inch.
How far will a horizontal stream travel if pressure is 45 pounds per square inch and the nozzle diameter is 1.75 inches? (Round your answer to one decimal place.)
(Of course... all of these answers are wrong... what am I doing?)