SOLUTION: A bridge is to be built across a waterway which is 50 feet wide and is frequented by ships. The bridge design team determines that a parabolic opening underneath the bridge is th

Question 889534: A bridge is to be built across a waterway which is
50 feet wide and is frequented by ships. The bridge design team determines that a parabolic
opening underneath the bridge is the best possible option for both structure and functionality
(keeping the waterway passable by ships while still being safe for vehicles to travel across).
If parabolic opening touches the ground right at the edges of the waterway and the maximum
height of the opening is 60ft, what is the maximum height that a 20-foot wide boat could be
and still pass through the opening?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bridge is to be built across a waterway which is
50 feet wide and is frequented by ships. The bridge design team determines that a parabolic
opening underneath the bridge is the best possible option for both structure and functionality
(keeping the waterway passable by ships while still being safe for vehicles to travel across).
If parabolic opening touches the ground right at the edges of the waterway and the maximum
height of the opening is 60ft, what is the maximum height that a 20-foot wide boat could be
and still pass through the opening?
:
Using the form ax^2 + bx + c = y
have the axis of symmetry at the origin, then c = 60
x intercepts occur at x = -25 and x = +25
Two equations
-25^2(a) -25b + 60 = 0
625a - 25b + 60 = 0
and
+25^2(a) + 25b + 60 = 0
625a + 25b + 60 = 0
:
Use elimination, add the two equations
625a - 25b + 60 = 0
625a + 25b + 60 = 0
-------------------- adding eliminates b find a
1250a + 120 = 0
1250a = - 120
a = -120/1250
a = -.096
The equation
y = -.096x^2 + 60
looks like this

20' wide boat can be represented by the distance between -10 and +10
Find the height at these points
y = -.096(10^2) + 60
y = -.9.6 + 60
y = 50.4 ft
a 50 ft high boat would just be able pass through (green line)

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