Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 70 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.)

Answer 1

Answer:

  17.5 m

Step-by-step explanation:

The height of a parabola above its vertex is proportional to the square of the distance from the vertex.

Cable height

The towers are 1200 m apart, so each is 600 m from center. The location of interest is 300 m from center, so 1/2 the distance to a tower. Since the height is proportional to the square of the distance, the height half-way to the tower will be (1/2)² = 1/4 the height of the tower.

  (1/2)²×(70 m) = 17.5 m

The height of the cable 300 m from center will be 17.5 meters.