A squirrel has 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 squirrels height above the ground.
A. The quotient that describes the rate of change in the squirrels height above the ground is 10.48feet/second
B. The quotient that describes the rate of change in the squirrels height above the ground is 19.05feet/second
C. The quotient that describes the rate of change in the squirrels height above the ground is -10.48feet/second
D. The quotient that describes the rate of change in the squirrels height above the ground is -19.05feet/second
The quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/second.
To find the rate of change in the squirrel's height above the ground, we can use the formula:
Rate of change = change in height / time taken
The squirrel starts on a perch 100 feet above the ground and moves down to its stored acorns in 5.25 seconds. The change in height is given by:
Change in height = final height - initial height
Change in height = 45 feet - 100 feet
Change in height = -55 feet
Now, we can calculate the rate of change:
Rate of change = -55 feet / 5.25 seconds
Simplifying:
Rate of change = -10.48 feet/second
Thus, the correct option is:
C. The quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/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 change in time.
First, let's calculate the change in height. The squirrel starts on a perch 100 feet above the ground, and its stored acorns are 45 feet from the ground. So, the initial height is 100 feet, and the final height is 45 feet.
Change in height = Final height - Initial height
Change in height = 45 feet - 100 feet
Change in height = -55 feet
Next, let's calculate the change in time. The squirrel takes 5.25 seconds to move from the perch to its stored acorns.
Change in time = 5.25 seconds
Now, let's divide the change in height by the change in time to find the rate of change.
Rate of change = Change in height / Change in time
Rate of change = -55 feet / 5.25 seconds
Rate of change ≈ -10.48 feet/second
Therefore, the quotient that describes the rate of change in the squirrel's height above the ground is approximately -10.48 feet/second. Therefore, the correct answer is C. The quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/second.