Sure, let's break down the problem step by step to find the average height change per horizontal foot for the roller coaster.
1. Identify the given values:
- The horizontal distance over which the height changes is 25 feet.
- The height change from the top of the drop to the bottom is -125 feet.
2. Set up the expression for average height change per horizontal foot:
The average height change per horizontal foot can be found by dividing the total height change by the horizontal distance over which this change occurs.
3. Calculate the average height change per foot:
[tex]\[
\text{Average height change per foot} = \frac{\text{Total height change}}{\text{Horizontal distance}}
\][/tex]
Substituting the given values, we get:
[tex]\[
\text{Average height change per foot} = \frac{-125 \text{ feet}}{25 \text{ feet}}
\][/tex]
4. Simplify the calculation:
[tex]\[
\text{Average height change per foot} = -5 \text{ feet}
\][/tex]
Therefore, the average amount that the roller coaster's height changes over each horizontal foot is [tex]\(-5\)[/tex] feet.
Among the given options:
- [tex]\(\frac{1}{5} \, \text{ft}\)[/tex]
- [tex]\(-\frac{1}{5} \, \text{ft}\)[/tex]
- [tex]\(-5 \, \text{ft}\)[/tex]
- [tex]\(5 \, \text{ft}\)[/tex]
The correct answer is [tex]\(-5 \, \text{ft}\)[/tex].
