Question

a falling object travels a distance given by the formula d=5t + 16t^2 ft, where t is measured in seconds. how long will it take for the object to traveled 74 ft?

Answer 1

Its given that

$d=5t+16t^{2}$

We need to find t when d = 74

Therefore, $74=5t+16t^{2}$ or

$16t^{2}+5t-74 = 0$

$16t^{2}+37t-32t-74 = 0$

t(16t + 37) - 2(16t + 37) = 0

(t - 2)(16t + 37) = 0

t - 2 = 0 or 16t + 37 = 0

t couldn't be negative.

Therefore, t = 2

Hence, it will take 2 seconds for the object to travel 74 feet.

Answer 2

Answer:

The time it will take for the object to traveled 74 ft is:

                   $t=2\ seconds$

Step-by-step explanation:

The formula which represents the distance traveled by a falling objectin time t is given by:

            $d=5t+16t^2$

Now, we are asked to find the time t required by the object in order to travel the distance of 74 ft.

i.e. we are asked to find t when d=74 ft.

i.e.

$16t^2+5t=74\\\\16t^2+5t-74=0$

Now, we know that any quadratic equation of the type:

           $ax^2+bx+c=0$

is solved using the quadratic formula:

      $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here,

$a=16\ ,\ b=5\ and\ c=-74$

Hence, on putting these value in the formula we have:

 $t=-2.313\ and\ t=2$

Since, the time can't be negative.

Hence, we have:

          $t=2$