A squirrel has stored its acorns and 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 purge down to stored acorns in 5.25 seconds quotient to describe the rate of change the squirrels height above the ground your answer to the nearest hundred.

Answer 1

To find the rate of change of the squirrel's height above the ground as it descends to its stored acorns, we can start by determining the total change in height and then divide that by the time taken.

1. Initial height: The squirrel starts at a perch that is 100 feet above the ground.
2. Final height: The squirrel reaches its stored acorns at a height of 45 feet above the ground.
3. Change in height: \[ \text{Change in height} = \text{Initial height} - \text{Final height} = 100 \text{ feet} - 45 \text{ feet} = 55 \text{ feet} \]
4. Time taken: The squirrel takes 5.25 seconds to descend.

Now we can calculate the rate of change in height: \[ \text{Rate of change} = \frac{\text{Change in height}}{\text{Time}} = \frac{55 \text{ feet}}{5.25 \text{ seconds}} \approx 10.48 \text{ feet per second} \]

Rounding this to the nearest hundredth gives us: \[ \text{Rate of change} \approx 10.48 \text{ feet per second} \]

So, the squirrels' rate of change of height above the ground is approximately 10.48 feet per second.