A bridge is to be constructed to pass over a road, and a surveyor is sent to take some measurements to determine how tall the bridge needs to be. She takes the positive z-axis to y-axis to be north, and the z-axis to be altitude, all measured in metres. In this coordinate system, the road can be modelled by the straight line passing through the points O: (r.y. 2) = (0,0,0) and A: (z, y, z) = (23, 1200, 49). The bridge and can modelled by the straight line passing through the point B: (z, y, z)=(-46,906, h) and C: (x, y, z) = (37,906, h), where his one east, the positive some value that is to be determined. Road safety regulations require that the bridge must be at 6 metres away from the road at all points. In order to minimise construction costs, what is the smallest possible value of h? t leas?
A bridge is to be constructed to pass over a road, and a surveyor is sent to take some measurements to determine how tall the bridge needs to be. She takes the positive z-axis to y-axis to be north, and the z-axis to be altitude, all measured in metres. In this coordinate system, the road can be modelled by the straight line passing through the points O: (r.y. 2) = (0,0,0) and A: (z, y, z) = (23, 1200, 49). The bridge and can modelled by the straight line passing through the point B: (z, y, z)=(-46,906, h) and C: (x, y, z) = (37,906, h), where his one east, the positive some value that is to be determined. Road safety regulations require that the bridge must be at 6 metres away from the road at all points. In order to minimise construction costs, what is the smallest possible value of h? t leas?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A bridge is to be constructed to pass over a road, and a surveyor is sent to take some measurements
to determine how tall the bridge needs to be. She takes the positive z-axis to east, the positive
y-axis to be north, and the z-axis to be altitude, all measured in metres.
thro 22%
the points
In this coordinate system, the road can be modelled by the straight line
O: (r, y, z) = (0,0,0) and A: (r, y, z) = (23, 1200, 49). The bridge and can modelled by the straight
line passing through the point B: (z. y, z)=( and C: (r. y, z) = (37,906, h), where his
some value that is to be determined.
Road safety regulations require that the bridge must be at least 6 metres away from the road at all
points. In order to minimise construction costs, what is the smallest possible value of h?
lleg
Coll
Mor
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