Question

A tunnel has a parabolic cross-section. It is 24m wide at the base. At a point 6m above the base, the width is 18m. Find the maximum height of the tunnel

Answer 1

13.71 m

Explanation:

Draw the tunnel so the width marks the zeroes at (-12,0) and (12,0)

then y = a ( x+12)(x-12) is the equation..

..to calculate 'a' sub in the point 9, 6 (where the width is 18)

6 = a ( (9+12)(9-12) shows a = -2/21

y = -2/21 (x+12)(x-12) Max is when x = 0

-2/21 ( 12)(-12) = 288/21 = 13.71 m