Horizontal reach of straight streams: 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 reach of straight streams: 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.

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

Here p is pressure in pounds per square inch. How far will a horizontal stream travel if the pressure is 50 pounds per square inch and the nozzle diameter is 1.75 inches?

d. Firefighters have a nozzle with a diameter of 1.25 inches. The pumper generates a pressure of 70 pounds per square inch. The hose nozzle is 75 feet from a fire. Can a horizontal stream of water reach the fire?