Question

An object is dropped from a building and allowed to freefall to the ground. The height of the object over time is shown in the table. (For reference: h(t) = 144 – 16t2) Time (seconds) Height (feet) 0 144 1 128 2 80 3 0 Which statement describes the rate of change of the height of the object over time? The rate of change is constant with the object dropping 1 foot every second. The rate of change is constant with the object dropping 144 feet every second. The rate of change decreases over time. The object is 128 feet above ground after one second, but 80 feet after two seconds. The rate of change increases over time. The object drops 16 feet in the first second, but 80 feet in the last second.

Answer 1

To find how long it will take the object to hit the ground, set the equation equal to 00=144-16t² *add 16t² to both sides*16t²=144 *divide both sides by 16*t²=9 *take the square root of both sides*t=3It will take three seconds for the object to hit the groundHope this helps

Answer 2

Answer: The (magnitude of the) rate of change increases over time. The object drops 16 feet in the first second, but 80 feet in the last second.

Explanation:

1) I will start by showing the table in an easy way to read and understand:

Time (seconds)   Height (feet)

0                           144

1                            128

2                           80

3                             0

2) Rate of change

• An initial clarification: the rate of change decreases since it is becoming more negative every second, but, in the analysis, the reasonable is to deal with the magnitude of this rate. The results shown below that the rate as a negative value, but the comparison is set about the magnitude of the change.

• The rate of change is calculated for every pair of consecutive points using this equation:

          rate of change = [change in height] / [time elapsed]

• Calculations:

a) rate₁: [128 - 144] feet / [ 1 - 0] sec = - 16 feet / sec ⇒ the object drops 16 feet in the first second.

b) rate₂ = [80 - 128] feet / [2 - 1] sec = - 48 feet/sec ⇒ the object drops 48 feet in the next second

c) rate₃ = [0 - 80] feet / [3 - 2] sec = - 80 feet/sec ⇒ the object drops 80 feet in the last second.

The rate of change  is more negative every second: it increases in magnitude over time. The object drops 16 feet in the first second, but 80 feet in the last second.