A suspension bridge with weight uniformly distributed along its length has twin towers that extend 95 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. (Assume that the road is level.)
Accepted Solution
A:
Answer:Height = 23.75 metresStep-by-step explanation:The Twin Towers are 1200 metres apart. This means that the centre point of the two towers is 1200/2 = 600metresSince the cables are parabolic in shape, we will use the parabola equation y = ax^2y = 95 metres x = 600 metres Put x and y into the equation. We have 95 = a(600)^2a = 95/600^2a = 95/ 360000a = 19/72000Therefore, y = (19/72000)x^2To find the height of the cable at 300 metres from the center, it means x is now equal 300 metresRecall that y = (19/72000)x^2y = (19/72000)300^2y = (19*300*300)/72000y = (19*90000)/72000y = 23.75The height is 23.75 metres