Question

Engineers are designing a rollercoaster that at one point goes underground. The rollercoaster’s path underground is a large curve. The engineers use the function shown to model the elevation, ܧ ,in feet and ݐ , time, in seconds, of the rollercoaster’s path while it is underground.

Answer 1

The question is about calculating the speed of a roller coaster at the top of a loop given the radius and a specific downward acceleration. The acceleration is 1.50 times the gravitational acceleration and the radius is 15 meters. Using the formula for centripetal acceleration, we can determine the speed.

• The student's question is related to the physics principles used in the designing of roller coasters.
• Specifically, it involves calculating the speed of the roller coaster at the top of a loop with a given radius and specified downward centripetal acceleration.
• The downward centripetal acceleration at the top of the loop is greater than the acceleration due to gravity to keep the passengers securely seated.
• Using physics, we can calculate the speed using the formula for centripetal acceleration a = v^2/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of curvature.
• To find the speed at the top of the loop where the radius r is 15.0 m and acceleration is 1.50 g (where g is the acceleration due to gravity, 9.8 m/s2), we need to set the centripetal acceleration equal to 1.50 times the gravitational acceleration.
• Hence a = 1.50 * 9.8 m/s2 = 14.7 m/s2.
• The equation becomes 14.7 m/s2 = v^2 / 15.0 m.
• Solving for v, we get the speed at the top of the loop.

Answer 2

One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:

(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3

Explanation:

One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:

(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3