Question

the table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. falling object
time (sec) x 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.6
height (m) h 100 93.8 95.1 89.0 80.4 69.4 55.9 40.0 21.6 0
a line of best fit for the data is represented by h = -21.962x + 114.665. which statement compares the line of best fit with the actual data given by the table?
according to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
the line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.
the line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.

Explanation:

Step1: Find line's ground time

Set h=0: 0=-21.962x+114.655 → x≈114.655/21.962≈5.22s

Step2: Actual ground time

From table: 4.6s

Step3: Time difference

5.22-4.6≈0.6s

Step4: Check 40m at 3.5s

Line predicts h=-21.962*3.5+114.655≈37.79m≠40m

Step5: Check height difference

At x=1.0, line predicts 92.693m < actual 95.1m (not greater)

Answer:

A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.