The road is centered on the axis of symmetry and the transport truck must stay on its own side of the road. Can the transport truck safely pass through the bridge?  Justify your decision using a clearly constructed mathematical model.
in Word Problem Answers by
reshown by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The general equation of a parabola where the axis of symmetry is the y-axis has the form y-k=ax², where k is the y-intercept, and the vertex is (0,k). The highest point of the arch is 10m above the ground and this point is the vertex, so k=10. We have y=ax²+10. The ground width of the arch is 16m, which means that the x-intercepts are -8 and 8. Therefore x²=64 and y=0, so:

0=64a+10. Therefore, a=-10/64=-5/32, making y=10-5x²/32.

The truck must stay on its correct side of the road so, since we know its height is 3.5m, the distance between this height and the arch wall must exceed the width of the truck (5m) at this height, otherwise the truck cannot keep to its own side of the road and avoid hitting the arch wall.

The height corresponds to the y value, so we can calculate the corresponding x value:

3.5=10-5x²/32, x²=32×(10-3.5)/5=32×1.3=41.6m².

x=6.45m approx.

The truck is 5m wide so it has clearance of about 1.45m and will be able to pass under the arch.

by Top Rated User (816k points)

Related questions

0 answers
asked May 1, 2013 in Geometry Answers by anonymous | 655 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,016 questions
91,947 answers
23,907 users