Question 893728: When the load is uniformly distributed horizontally, the cable of a suspension bridge hangs in a parabolic arc. If the supporting towers are 60 ft high and 300 ft apart and the cable hangs 20 ft above the roadbed at the center, find the equation of the parabola that best describes the shape of the cable. Then determine the distance from the roadbed to the cable at interval of 50 ft.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! When the load is uniformly distributed horizontally, the cable of a suspension bridge hangs in a parabolic arc. If the supporting towers are 60 ft high and 300 ft apart and the cable hangs 20 ft above the roadbed at the center, find the equation of the parabola that best describes the shape of the cable. Then determine the distance from the roadbed to the cable at interval of 50 ft.
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set vertex at origin, 20 ft above center of roadbed
Basic form of equation for a parabola that opens upwards as in this case:
x^2=4py
using coordinates of point where cable is supported 40 ft above vertex and 150 ft from center of roadbed
x^2=4py
4p=x^2/y=150^2/40=562.5
..
at 50 ft from center:
y=x^2/4p=50^2/562.5=4.44 ft above vertex or 20+4.44=24.44 ft above roadbed.
distance from the roadbed to the cable 50 ft. from center=24.44 ft
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