Question

The cable of a suspension bridge has supporting towers which are 50 ft high and 400 ft apart and is in the shape of a parabola.If the lowest point of the cable is 10 ft above the floor of the bridge, find the length of a supporting rod 100 ft from the center of the span.

Answer 1

Since the vertex is at (0,10), we know that
y = ax^2 + 10
Now, since y(200) = 50,
40000a + 10 = 50
a = 1/1000

at x=50,
y = 1/1000 * 2500 + 10 = 12.5

Answer 2

rats. at x=100,
y = 1/1000 * 100^2 + 10 = 20