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): { ( 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 ) }
Step 4: Determine the height from which the egg was launched.
8 feet
3 feet
16 feet
0 feet
The Correct Answer and Explanation is :
The correct answer is: 16 feet
To determine the height from which the egg was launched, we need to analyze the provided data points that indicate the height of the egg at various time intervals. The data set is as follows:
- At ( t = 0.0 ) seconds, the height is ( 16 ) feet.
- At ( t = 1.7 ) seconds, the height is ( 20.46 ) feet.
- At ( t = 2.5 ) seconds, the height is ( 23.16 ) feet.
- At ( t = 3.7 ) seconds, the height is ( 23.51 ) feet.
- At ( t = 5.1 ) seconds, the height is ( 20.07 ) feet.
- At ( t = 6.6 ) seconds, the height is ( 12.4 ) feet.
- At ( t = 7.3 ) seconds, the height is ( 5.62 ) feet.
- At ( t = 8.0 ) seconds, the height is ( 0.15 ) feet.
The initial height of the egg can be directly determined from the first data point. At ( t = 0.0 ) seconds, the height is ( 16 ) feet. This indicates that the egg was launched from a height of ( 16 ) feet above the ground.
To further understand the motion, we can analyze the trajectory of the egg. The data shows that the egg reaches its peak height of ( 23.51 ) feet at ( t = 3.7 ) seconds before starting to descend. This ascent and subsequent descent follow the principles of projectile motion, where an object rises to a peak height before being pulled back down by gravity.
As time progresses, the height decreases, reaching ( 0.15 ) feet just before it hits the ground at ( t = 8.0 ) seconds. This motion indicates that the egg was launched upward from its initial height, reached a maximum height, and then fell back down.
In conclusion, the height from which the egg was launched is clearly given in the data as 16 feet. This is the height recorded at ( t = 0.0 ) seconds, confirming that the egg started its trajectory from that elevation.