A firefighter mounts the nozzle of his fire hose a distance 36.9 m away from the edge of a burning building so that it sprays from ground level at a 45° angle above the horizontal. After quenching a hotspot at a height of 8.85 m, the firefighter adjusts the nozzle diameter so that the water hits the building at a height of 17.9 m. By what factor was the nozzle diameter changed? Assume that the diameter of the hose stays the same, and treat the water as an ideal fluid.

Question

Giovanna Ellis

Physics

26 March, 12:16

A firefighter mounts the nozzle of his fire hose a distance 36.9 m away from the edge of a burning building so that it sprays from ground level at a 45° angle above the horizontal. After quenching a hotspot at a height of 8.85 m, the firefighter adjusts the nozzle diameter so that the water hits the building at a height of 17.9 m. By what factor was the nozzle diameter changed? Assume that the diameter of the hose stays the same, and treat the water as an ideal fluid.

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Answers (1)

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Cassidy Sanford · Answer 1

If you visualize the problem, there are two corresponding angles with the same base of 36.9 m. The angle is 45 degrees for a height of 8.85 m. We have to find, what is the angle when the height is 17.9 m? Since the base is known to be 36.9 m and the height is known to be 17.9 meters, we could use the tangent function. Let the angle be X.

X = arctan (17.9/36.9)

X = 25.9 degrees

The ratio or the factor of change would be 45/25.9 = 1.7

Therefore, the factor is 1.7.