Question

A bridge on a river is modeled by the equation h = -0.2d^2 + 2.25d, where h is the height and d is the horizontal distance. For cleaning and maintenance purposes a worker wants to tie a taut rope on two ends of the bridge so that he can slide on the rope. The rope is at an angle defined by the equation -d + 6h = 21.77. If the rope is attached to the bridge at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point A?

Answer 1

We are given the equations
h = -0.2d² + 2.25d
-d + 6h = 21.77

Solving for d in the second equation:
-d + 6h = 21.77
d = 6h - 21.77
Substituting to the first equation:
h = -0.2(6h - 21.77)² + 2.25(6h - 21.77)
The value of h can then be solved with is
h = 3.9968
so
d = 2.2108