Parabolic function word problem

Question

A truck with a height of 190m enters a tunnel with a parabolic ceiling the width of the tunnel is 20m and the maximum height of the tunnel is 10m. At what minimal distance from the edge at ground level can this truck pass through the tunnel?

Answer 1

No truck has a height of 190 m. Realistically, it 's more like 1.90 m. This latter value will be used in the s0lution to the problem.

 

Let the center of the tunnel and on the ground be the origin. Then the roots of the quadratic function are

x = +10, -10

The equation of the parabola is of the form

y = A(x-10)(x+10)

To solve for A, note that when x = 0, y = 20.

A = -1/10 = - 0.1

 

y = - 0.1 (x-10)(x+10)

The truck's height is 1.9 m

Substitute y = 1.9 and solve for x.

x =9

 

One edge of the tunnel is 10 m from the center. Therefore the truck can pass through this tunnel at a minimal distance of 10-9 = 1m

Answer 2

A truck with a height of 190 m cannot enter a tunnel with maximum height of 10 m!