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	98.8	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 + 114.655. 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.
according to the line of best fit, the object was dropped from a lower height.
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: Encontrar el tiempo real de impacto

En la tabla, el objeto toca el suelo en $x = 4.6$ segundos.

Step2: Encontrar el tiempo de impacto predicho

Establecemos $h = 0$ en la ecuación $h=-21.962x + 114.655$. Entonces, $0=-21.962x + 114.655$. Re - arreglamos: $21.962x=114.655$, y $x=\frac{114.655}{21.962}\approx5.2$ segundos.

Step3: Comparar los tiempos

El tiempo de impacto predicho es $5.2$ segundos y el tiempo real es $4.6$ segundos. La diferencia es $5.2 - 4.6=0.6$ segundos. Entonces, el objeto se predice que toca el suelo 0.6 segundos después del tiempo real.

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.