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.)

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.)