Chapter 2, Problem 33P

A level pipeline is required to pass through a hill having a parabolic profile

$y=-0.005x^2+0.35x.\left(2.75\right)$

The origin of the x - and y -coordinates is fixed at elevation zero near the base of the hill, as shown in Fig. P2.33.

(a) Write the quadratic equation for a pipeline elevation of $y=3$ m.

(b) Solve the quadratic equation found in part (a) to determine the positions of the tunnel entry X_A and exit X_b using both the quadratic formula and completing the square.

(c) Find the length of the tunnel.