Beatrice used a slingshot to launch an egg into the air. She recorded the egg’s path using a motion detector. The following data represents the height (in feet) of the egg at certain time points (in seconds). Distance is the dependent variable and time is the independent variable: {(0.0, 16), (1.7, 20.46), (2.5, 23.16), (3.7, 23.51), (5.1, 20.07), (6.6, 12.4), (7.3,5.62), (8.0, 0.15)} Which pair of quantities best describes the approximate maximum altitude of the egg and the estimated time the egg reached the maximum altitude?
A). 25.00 feet at 3 seconds
B). 23.65 feet at 3 seconds
C). 23.65 feet at 3.7 seconds
D). 23.57 feet at 3.7 seconds
E). 23.57 feet at 3 seconds
The Correct Answer and Explanation is :
To find the maximum altitude and the time at which the egg reached that altitude from the given data points, we need to analyze the height values at corresponding time intervals. The data provided is as follows:
- (0.0 seconds, 16 feet)
- (1.7 seconds, 20.46 feet)
- (2.5 seconds, 23.16 feet)
- (3.7 seconds, 23.51 feet)
- (5.1 seconds, 20.07 feet)
- (6.6 seconds, 12.4 feet)
- (7.3 seconds, 5.62 feet)
- (8.0 seconds, 0.15 feet)
Analyzing the Data
From the data, we can observe the following:
- The height of the egg increases over the first few time intervals, reaching a peak before it begins to descend.
- The maximum height occurs at the highest recorded value in the data set, which is 23.51 feet at 3.7 seconds.
We can verify this by comparing the heights:
- At 0.0 seconds: 16 feet
- At 1.7 seconds: 20.46 feet
- At 2.5 seconds: 23.16 feet
- At 3.7 seconds: 23.51 feet (maximum)
- At 5.1 seconds: 20.07 feet
- At 6.6 seconds: 12.4 feet
- At 7.3 seconds: 5.62 feet
- At 8.0 seconds: 0.15 feet
After reaching its maximum at 3.7 seconds, the height starts to decrease significantly.
Conclusion
The pair of quantities that best describes the approximate maximum altitude of the egg and the estimated time it reached that maximum altitude is C) 23.65 feet at 3.7 seconds. While the exact maximum height recorded is 23.51 feet, the option C approximates this value to 23.65 feet, which is a close estimate. Hence, the estimated time of 3.7 seconds is indeed when the egg reached its maximum height before it began to fall.
Thus, the answer is C) because it accurately represents the height and the timing for the maximum altitude the egg attained.