SOLUTION: A park has a water channel with a semicircular cross section that has a radius of 13ft. The boats that are to be used in this water system have rectangular cross sections and are k

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Question 1120557: A park has a water channel with a semicircular cross section that has a radius of 13ft. The boats that are to be used in this water system have rectangular cross sections and are known to submerge 2 ft into the water. If the water channel is to be filled with water 7.5ft deep, what is the maximum possible width of the boats?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52799) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
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A park has a water channel with a semicircular cross section that has a radius of 13ft. The boats that are to be used in this water system have rectangular cross sections and are known to submerge 2 ft into the water. If the water channel is to be filled with water 7.5ft deep, what is the maximum possible width of the boats?
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If you mean filled with water to a level of 7.5 feet:
The bottom of the boat would be 5.5 feet about the center of the channel and 7.5 feet from the top of the channel.
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With the Origin at the center of the top of the channel, the equation of the circle is x%5E2+%2B+y%5E2+=+13%5E2
The bottom of the boat is on the line y = -7.5
x%5E2+%2B+%28-7.5%29%5E2+=+169
x^2 = 112.75
x = ~10.62 feet
Width = ~21.24 feet maximum