Question

A squirrel has stored its acorns in a hole hole that is 45 feet from the ground in a tall tree. The squirrel starts on a perch, 100 feet above the ground. The squirrel moves from the perch down to its stored acorns in 5.25 seconds. Interpret the quotient to describe the rate of change and the squirrels height above the ground. Give your answer to the nearest hundredth.

Answer 1

To find the rate of change in the squirrel's height above the ground while it moves from its perch to the stored acorns, we first need to calculate the difference in height and divide that by the time taken.

1. **Initial height (from the perch)**: 100 feet
2. **Final height (where the acorns are stored)**: 45 feet
3. **Change in height**:

\[
\text{Change in height} = \text{Initial height} - \text{Final height} = 100 \text{ ft} - 45 \text{ ft} = 55 \text{ ft}
\]

4. **Time taken**: 5.25 seconds

5. **Rate of change**:

\[
\text{Rate of change} = \frac{\text{Change in height}}{\text{Time}} = \frac{55 \text{ ft}}{5.25 \text{ s}}
\]

Now, let's do the calculation:

\[
\frac{55}{5.25} \approx 10.4762
\]

Rounding to the nearest hundredth, the rate of change in height is:

\[
10.48 \text{ feet per second}
\]

This means that the squirrel is descending at a rate of approximately **10.48 feet per second** as it moves from the perch to its stored acorns.