a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide. Assuming a truck is 12ft wide, what is the tallest truck that can pass under the overpass
Answers
Given : a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide
truck is 12ft wide
To Find : what is the tallest truck that can pass under the overpass
Solution:
Let say ellipse is
x²/a² + y²/b² = 1
Width is 20 ft
=> 2a = 20
=> a = 10
Height is 15 ft
=> b = 15
x²/10² + y²/15² = 1
truck is 12ft wide
hence maximum height of truck when x = - 6 and 6
x²/10² + y²/15² = 1
=> 6²/10² + y²/15² = 1
=> y²/15² = 8²/10²
=> y = 15 (0.8)
=> y = 12
tallest truck that can pass under the overpass = 12 ft
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