A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by h ( x ) = − 0.026 x 2 + 0.577 x + 3 , where h ( x ) is the height of the water in meters at a point x 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 to 1 decimal place. b. What is the maximum height of the water? Round to 1 decimal place. c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by h ( x ) = − 0.026 x 2 + 0.577 x + 3 , where h ( x ) is the height of the water in meters at a point x 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 to 1 decimal place. b. What is the maximum height of the water? Round to 1 decimal place. c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
Solution Summary: The author calculates the horizontal distance from the firefighter at which the water will be at its maximum height.
A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 308. The height of the water can be approximated by
h
(
x
)
=
−
0.026
x
2
+
0.577
x
+
3
, where
h
(
x
)
is the height of the water in meters at a point x 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 to 1 decimal place.
b. What is the maximum height of the water? Round to 1 decimal place.
c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. How far is the firefighter from the house? Round to the nearest meter.
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