Question

The cable of a suspension bridge hangs in the shape of a parabola . The towers supporting the cable are 400 ft apart and 150 ft high. If the cable , at its lowest , 30 ft above the bridge at its midpoint , how high is the cable 50ft away (horizontally) from either tower?

Answer 1

Let the lies in the middle between two towers.

The equation of parabola will be $y=ax^2+b.$

$y(0)=30\to b=30.$

$y(200)=150\to 40000a+30=150\to a=\frac{120}{40000}=0.003.$

Thus, the equation of parabola: $y=0.003x^2+30.$

$y(200-50)=y(150)=0.003*150^2+30=97.5.$

The cable is 97.5 ft high 50 ft away from either tower.