You see a firefighter aim a fire hose from 4 feet above the ground at a window that is 26 feet above the ground. The equation h=-0.01d^2+1.06d+4 models the path of the water when h equals height in feet. Estimate, to the nearest whole number, the possible horizontal distances (d) in feet between the firefighter and the building.

Question

You see a firefighter aim a fire hose from 4 feet above the ground at a window that is 26 feet above the ground.  The equation h=-0.01d^2+1.06d+4 models the path of the water when h equals height in feet. Estimate, to the nearest whole number, the possible horizontal distances (d) in feet between the firefighter and the building.

been out of school for a while and can remember how to do this. if cant give the answer, instructions on how to would be much appreciated.

bobpursley · Answer

26=-.01d^2+ 1.06d+ 4
.01d^2-1.06d -22=0
multiplying by 100
d^2-106d-2200=0

Now use the quadratic equation..

d=(106 +- sqrt (106^2+8800))/2

d= 53+- 1/2 sqrt (94)

You can work that out, normally the firefighter would work at the shorter distance, but both are possible.