Question

The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

Write the equation that models the height of the roller coaster.

Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points)

Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)
Copyright© E2020, Inc. 2011 1
Copyright© E2020, Inc. 2011

Worksheet (continued)

Roller Coaster Design
Worksheet








Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below or sketch a graph by hand. (5 points)

Answer 1

1) Equation of the circle (centered at the origin): x^2 + y^2 = r^2.
The highest point of the top half is at (0,r) and is 30 ft above ground, so r = 30.
Thus: x^2 + y^2 = 30^2 = 900.

2) Solve for y (positive root only, since the coaster is above ground):
y = sqrt(900 − x^2), with domain −30 ≤ x ≤ 30.

This y = sqrt(900 − x^2) models the height (in feet) of the top half of the circular coaster section.