A firefighter holds a hoose 2 m off the ground and directs a stream of water tow

Question

A firefighter holds a hoose 2 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 14 m/sec at an angle of 30 degrees. The height of the water can be approximated by (x)=-0.25x^2+0.540x+2, where h(x) is the height of the water in meters at a point meters horizontally from the firefighter to the building.

A. Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. Round 1 decimal place.

B. What is the maximum height of the water? Round to 1 decimal place.

Explanation / Answer

h(x) = -0.25x^2 + 0.540x + 2

a) horizontal distance at which maximum height occurs is

x = - 0.540 / 2 ( -0.25 )

x = 1.1 m

b) maximum height = - 0.25 ( 1.1)^2 + 0.540 (1.1) + 2

maximum height = 2.3 m

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