A squirrel has stored its acoms 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)
To find the rate of change in the squirrel's height above the ground, we need to divide the change in height (from the perch to the stored acorns) by the time taken.
The change in height is equal to the starting height minus the final height.
Starting height = 100 feet
Final height = 45 feet
Change in height = 100 ft - 45 ft = 55 ft
The time taken is 5.25 seconds.
Rate of change in height = Change in height / Time taken
= 55 ft / 5.25 s
≈ 10.48 ft/s
Therefore, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.
Is it negative or positive
Apologies for the confusion in my previous response. The sign of the rate of change depends on the reference point chosen.
If we consider the starting height of the squirrel (100 feet) as the reference point, then the rate of change in the squirrel's height is positive because it is moving towards the stored acorns (45 feet).
If we consider the final height (45 feet) as the reference point, then the rate of change in the squirrel's height would be negative, indicating that it is moving away from the acorns.
Please let me know if there is anything else I can help you with.
So is is it -10.48
Yes, if we consider the final height (45 feet) as the reference point, then the rate of change in the squirrel's height would be -10.48 feet per second. It indicates that the squirrel is moving away from the stored acorns at a rate of approximately 10.48 feet per second.
To find the rate of change in the squirrel's height above the ground, we divide the change in height by the time it takes.
The change in height is 100 feet (starting from the perch) minus 45 feet (height of the stored acorns), which equals 55 feet.
The time taken is 5.25 seconds.
Now, we can calculate the rate of change:
Rate of change = Change in height / Time taken
= 55 feet / 5.25 seconds
Dividing these values, we get:
Rate of change ≈ 10.48 feet/second
Therefore, the rate of change in the squirrel's height above the ground is approximately 10.48 feet/second.
To determine the rate of change in the squirrel's height above the ground, we need to calculate the average speed at which the squirrel descends from its perch to the stored acorns. We can find the average speed by dividing the distance traveled by the time taken.
The distance traveled by the squirrel is the vertical distance from its perch to the stored acorns, which is 100 feet (the initial height of the squirrel's perch) minus 45 feet (the height of the stored acorns). So, the distance traveled is 100 - 45 = 55 feet.
The time taken is given as 5.25 seconds.
To calculate the average speed, divide the distance traveled (55 feet) by the time taken (5.25 seconds):
Average speed = distance / time
Average speed = 55 feet / 5.25 seconds
Using a calculator, we can find:
Average speed ≈ 10.47619 feet per second
Rounded to the nearest hundredth, the rate of change in the squirrel's height above the ground is approximately 10.48 feet per second.