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4.3.7Somepracticalproblems:Example 4.8:The girder of a railway bridge is in the parabolic form with span100 ft. and the highest point on the arch is 10 ft. above the bridge. Find the height othe bridge at 10 ft. to the left or right from the midpoint of the bridge.Solution |
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Answer» y = a(x-g)² + hLet x = 0 and y = 0 at the vertex of the parabola, the highest point of the arch at the midpoint of the bridge. Further, let y be positive in the downward direction so that y = 0 at the midpoint and 10 at the ends of the span where x = ±50.Then g = h = 0 and:y = ax² We know that y = 10 at x = ±5010 = a(±50)² = 2500aa = 10/2500 = 1/250 At x =±10, the height of the bridge will be h = 10-y(±10)h = 10 - 100/250 = 10 - 2/5 = 10-.4 = 9.6 ft |
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