Question

An expansion joint is designed to allow for a bridge to expand when it gets warm so that it does not buckle. The Silly Bridge was originally designed without expansion joints in it. The Silly Bridge is 2 miles long. Engineers predicted that during the summer months the Silly Bridge will expand 1 foot on both sides of the bridge. (Note: 1 mile = 5280 feet)

Assume that, when it expands, the road remains in a perfectly straight line from the base of the bridge to the center.

Part A. If the Silly Bridge expands 1 foot on both sides of the bridge, how high will the center of the bridge be (above the supports shown as the base in the diagram) when it fully expands due to heat? (The answer my surprise you.) Round your answer to the nearest whole foot. Be sure to show all work.

Part B. What will the angle of elevation be when the bridge is fully expanded? Be sure to show all work. ​

Answer 1

73 ft

0.79°

Explanation:

Original length of half bridge = 1 mile = 5280 ft

Length of half bridge after expansion = 1 mile + 1 ft / 2 = 5280.5 ft

h = height in the middle

5280.5² + h² = 5281²

h = √(27,888,961 - 27,883,680)

h = 73 ft

tan A = 73/5280.5

A = 0.79°