A triage with a semi clinical arch spans a river as shown he

A triage with a semi clinical arch spans a river as shown here what is the clearance 6 ft from the river bark? The durance 6 ft from the river bank is about ft.

Solution

It is a parabola and can be assumed that vertex is at (0, 12)

It is an inverted parabola: y = a( x- h)^2 +k

y = ax^2 +12

Now plug point which lies on parabola i.e ( -26 , 0) or ( 26 , 0)

So, 0 = a(26)^2 +12 ---->

a = -12/26*26 = -3/169

So, y = -3x^2/169 +12

Now find clearance 6 ft from the bank which means y for x = 20

So, y = -3(20)^2/169 +12 = 828/169 = 4.89 = 4.9 ft