A squirrel has stored its acorns in a 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 in the squirrel’s height above the ground. Give your answer to the nearest hundredth. please explain how you got the answer
To find the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time it took for the squirrel to make that change.
Change in height = 100 feet (starting height) - 45 feet (final height) = 55 feet
Time taken = 5.25 seconds
Rate of change in height = Change in height / Time taken
Rate of change in height = 55 feet / 5.25 seconds
Rate of change in height ≈ 10.48 feet/second
Therefore, the quotient, 10.48, represents the rate of change in the squirrel's height above the ground. This means that on average, the squirrel is moving downwards at a rate of approximately 10.48 feet per second.
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To determine the rate of change in the squirrel's height above the ground, we can calculate the average speed at which it descended from the perch to the stored acorns.
First, we need to find the difference in height between the perch and the stored acorns. The height of the tree (45 feet) and the perch (100 feet) are given, so we can find the vertical distance between them by subtracting the height of the stored acorns from the perch.
Vertical distance = height of perch - height of stored acorns
Vertical distance = 100 feet - 45 feet
Vertical distance = 55 feet
Next, we divide the vertical distance by the time it took for the squirrel to descend from the perch to the stored acorns.
Average speed = Vertical distance / Time
Average speed = 55 feet / 5.25 seconds
Using a calculator, we find that the average speed is approximately 10.48 feet per second.
Therefore, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.
To find the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time taken.
The initial height of the squirrel is 100 feet, and it descends to a height of 45 feet. The change in height is:
Change in height = 100 feet - 45 feet = 55 feet
The time taken for the descent is given as 5.25 seconds.
Now, we can calculate the rate of change by dividing the change in height by the time taken:
Rate of change = Change in height / Time taken
Rate of change = 55 feet / 5.25 seconds
To find the answer to the nearest hundredth, we can perform the division:
Rate of change = 10.476 <approximated to two decimal places> = 10.48 feet per second
Therefore, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.