The underside of a bridge has the shape of a parabolic arch. It has a max. Height of 20m and a width of 60m. A sail boat has a height of12m above the water. Can it safely pass under the bridge at a distance of 20m from the axis of simitry of the arch?


1 Answers

Oddman Profile
Oddman answered
You have not said what the height is at the ends of the bridge, so there is not enough information to answer the question.

If the height of the bridge is water level (0m) at a distance of 30m from center, the boat cannot pass. For that case, a suitable equation for the bridge height might be
  y = 20(1 - (x/30)^2)
For x=20, we have
  y = 20(1 - (20/30)^2) = 20(1 - 4/9) = 20*5/9 = 100/9 = 11.111...(repeating indefinitely)
The height of 11.1m at that point will not allow the 12m boat to pass.

A graph of this curve can be seen here.

If the bridge has a difference (d) in height between center and end of less than 18m, then the boat can safely pass. In other words, the ends of the bridge must be 2m or more above the water for the boat to have enough room.
  12 < 20 - d(20/30)^2    (an equation for height using "d" as a parameter)
  -8 < d(4/9)    (subtract 20)
  8*9/4 > d    (multiply by -9/4)
  18 > d    (evaluate)

Answer Question