Vertical reach of fire hoses: If a fire hose is held vertically, then the height the stream will travel depends on water pressure and on the vertical factor for the nozzle. The vertical factor V...

Vertical reach of fire hoses: If a fire hose is held vertically, then the height the stream will travel depends on water pressure and on the vertical factor for the nozzle. The vertical factor V depends on the diameter of the nozzle. For a 0.5-inch nozzle, the vertical factor is 85. For each 1 8 -inch increase in nozzle diameter, the vertical factor increases by 5.

a. Explain why the function giving the vertical factor V in terms of the nozzle diameter d is linear.

b. Use a formula to express V as a linear function of d (measured in inches).

c. Once the vertical factor is known, we can calculate the height S in feet that a vertical stream of water can travel by using

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

d. Firemen have a nozzle with a diameter of 1.25 inches. The pumper generates a pressure of 70 pounds per square inch. From street level, they need to get water on a fire 60 feet overhead. Can they reach the fire with a vertical stream of water?