The highest point of a roller coaster loop is 42 m and the lowest point is 18 m. If the height of a cart on the loop is modeled by a sine or cosine function, we need to find the amplitude.

1. Problem Description

The highest point of a roller coaster loop is 42 m and the lowest point is 18 m. If the height of a cart on the loop is modeled by a sine or cosine function, we need to find the amplitude.

2. Solution Steps

The amplitude of a sinusoidal function is half the difference between its maximum and minimum values.

Amplitude = $\frac{Maximum - Minimum}{2}$

In this case, the maximum height is 42 m and the minimum height is 18 m.

Amplitude = $\frac{42 - 18}{2}$

Amplitude = $\frac{24}{2}$

Amplitude = 12 m

3. Final Answer

12 m