Solve the problem 5 A crosssection of an irrigation canal is

Solve the problem. 5) A cross-section of an irrigation canal is a parabola. If the surface of the water is 17 feet wide and the canal is 2 feet deep at the center, how deep is it 1 feet from the edge?

Solution

equation of parabola is given by

y = ax^2

surface of water is 17 feet wide and canal is 2 feet deep

therefore, x = 17/2 = 8.5

y = 2

hence , 2 = a(8.5)^2

a = 2/ 8.5^2 = .02768

when x = 1

y = .02768 (1)^2 = .02768

therefore, it is 8.5 - .02768 = 8.47 feet deep from the edge