If air resistance is neglected, it can be shown that the stream of water emitted by a fire hose will have height

feet above a point located x feet from the nozzle, where m is the slope of the nozzle and v is the velocity of the stream of water as it leaves the nozzle. Assume v is constant.

a. Suppose m is also constant. What is the maximum height reached by the stream of water? How far away from the nozzle does the stream reach (that is, what is x when y = 0)?

b. If m is allowed to vary, find the slope that allows a firefighter to spray water on a fire from the greatest distance.

c. Suppose the firefighter is x = x₀ feet from the base of a building. If m is allowed to vary, what is the highest point on the building that the firefighter can reach with the water from her hose?

Transcribed Image Text:

y = -16(1 + m²) V 2 + mx