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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Physics

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8 July, 08:39

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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Martin Eaton · 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.