Bridge Problem?

Question

There is a bridge that goes across a river from shoreline to shoreline. The bridge is a perfect arch. A person walks 27ft across the bridge and stops to measure down to the surface of the water. The surface of the water is 9ft at 27ft across the bridge. He then goes to the midpoint of the bridge and measures again and finds that the surface of the water is at 10ft down from the midpoint of the bridge. How wide is the river?

Answer 1

EDIT: There was an error in my derivation file in my original post. It is now corrected.

The bridge could also be a circular arch; in that case the solution is more complex, but the answer (W=80) comes out pretty close to the parabolic case. The derivation is here: http://img371.imageshack.us/img371/3374/circulararchnh7.png

Technically, the 27ft should be measured along the arc of the bridge, and is not the horizontal distance. I'm sure the problem is not meant to be solved that way as the solution results in transcendental equations that must be solved numerically.

Answer 2

I'm assuming that "arch" means the curve is a parabola. The parabola starts with a height of zero and reaches a maximum height of 10.

90% of the height is reached at 27 feet. Since we have a parabolic function, the distance from this point to the midpoint is sqrt(1 - .9) of the total distance from the shore to the midpoint. This calculates to 31.6%.

So, 27 feet is 68.4% of the distance from the shore to the midpoint, which means the distance from the shore to the midpoint is 27 / .684 = 39.5 feet. The width of the river is double that, or 79 feet.

Answer 3

Because the answer for the circular arch comes out an exact number (see gp4rts answer above), that is what the problem probably intended.

Answer 4

the hearth Truck (consists of the mail that is going to the airport after it places out the hearth) The Ambulance (FBI agent & Diplomat journey w/ the ambulance so as that they could snag a journey on the different section)

Answer 5

w=75.1 m