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| Math Central | Quandaries & Queries |
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Subject: precalc A truck hauling a double-wide trailer needs to pass under a parabolic-arched bridge en route or take a 50 mile detour. The trailer is 14 feet high and 15 feet wide. The arch supporting the bridge at this underpass is 18 feet high at the center and 40 feet wide at the base. Can the trailer safely pass under the bridge? |
Hi Jim. Draw this on graph paper, with the x-axis representing the road and the origin the center of the road.
If you do this, you find that you have a parabola with Y intercept at (0,18), and x intercepts at (+/-20,0). You will need to estimate the curvature between the intercepts for now. That's the bridge overhead. Now draw a rectangle with corners at (+/-7.5,15) and (+/-7.5,0). That's the trailer. You are interested in knowing if the corners whack into the parabola or not.
The easiest way is to first come up with the equation for the parabola with these intercepts, then substitute x = +/-7.5 into it. If the value for y is greater than 15, then you should be safe, otherwise the trailer hits the bridge.
Hope this helps,
Stephen La Rocque.
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