The two towers are 2800 ft apart,The roadway is supported by 99 equal spaced cable systems between the two towers,The center cable is 10 ft long,the parabolic shaped cable is suspended from the top of each tower 310 ft,and the road way is horizontal.1)Find an equation of a parabolic curve that fits the given Information.2)Find the width of the interval between each cable.3)Find the length of the three cables to the right of the center cable.4)Find the length of the three cables closest to the tower.
Set up a cartesian coordinate system (Draw x and y axes on a sketch of the bridge) so that the roadway is represented by y 0 and the centre of the bridge is at x 0. This puts the towers at x -1400 ft and x +1400 ft You now have a parabola passing through the points (-1400,310); (0,10); (1400,310) The equation of that parabola is going to be in the form y ax? + c When x 0, y 10; so c 10 Substituting values for one of the suspension points: 310 a * (1400)? + 10 a 300 / (1400)? 1.53 * 10^-4 So y 0.000153x? + 10 99 cables plus the two towers will result in 100 intervals, so the interval will be 2800/100 28 ft So the three cables to the right of the centre cable will be at x 28, x 56 and x 84 Substitute each in turn into the equation for the parabola: Example: For the cable next to the centre cable, x 28 y 0.000153 * (28)? + 10 y 10.12 ft Repeat for the next two values of x The cable next to the tower will be at a value of x (1400 - 28) 1372 Next to that will be at x (1400 - 56) Next to that will be at x (1400 - 84) Just plug each value in turn into the equation.
