Question

If an object is dropped from a height of 45 feet, the function d = - 16t ^ 2 + 45 gives the height of the object after t seconds. Graph this function. Approximately how long does it take the object to reach the ground (d = 0) )?

Answer 1

The time taken by the object to reach the ground is
`1.677` (app.)

Step-by-step explanation:

The given function is
`d=-16 t^(2)+45`

To graph the function in the graph, let us substitute the values for t to find the value of d.

t d

0 45

1 29

2 -19

3 -99

4 -211

5 -355

These values are plotted in the graph which is attached below:

To determine the time it takes the object to reach the ground, let us substitute
`d=0` in the function
`d=-16 t^(2)+45`, we get,

`0=-16 t^(2)+45`

`-45=-16t^2`

`45=16t^2`

`2.8125=t^2`

`\pm1.677=t`

The value of t cannot be negative.

Thus,
`t=1.677` (app.)

Thus, the time taken by the object to reach the ground is
`1.677` (app.)