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.(1 point) Responses
The quotient that describes the rate of change in the squirrel’s height above the ground is −19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is −10.48 feet/second.
The quotient that describes the rate of change in the squirrel's height above the ground is 10.48 feet/second.
The correct interpretation of the quotient is: The quotient that describes the rate of change in the squirrel’s height above the ground is -19.05 feet/second.
To find the rate of change in the squirrel's height above the ground, we need to determine the change in height and the time it took for that change.
The squirrel starts at a perch 100 feet above the ground and moves down to its stored acorns, which are 45 feet from the ground. Therefore, the change in height is 100 - 45 = 55 feet.
The squirrel takes 5.25 seconds to move from the perch to the acorns.
To find the rate of change, we divide the change in height by the time it took: 55 feet / 5.25 seconds = 10.48 feet/second.
So the correct answer is:
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 calculate the change in height and divide it by the change in time.
The squirrel starts on a perch 100 feet above the ground and moves down to its stored acorns in a hole 45 feet from the ground. So the change in height is 100 - 45 = 55 feet (negative because the squirrel is moving downwards).
The squirrel takes 5.25 seconds to make this descent, so the change in time is 5.25 seconds.
Now, we can calculate the rate of change by dividing the change in height by the change in time:
Rate of change = (change in height) / (change in time)
= 55 feet / 5.25 seconds
= 10.476190476190476... feet/second
Rounding to the nearest hundredth, the rate of change in the squirrel's height above the ground is approximately 10.48 feet/second.
Therefore, the correct answer is:
The quotient that describes the rate of change in the squirrel's height above the ground is 10.48 feet/second.