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

Question

3 months ago

6

for the object to traveled 74 ft?

2 answers:

lawyer [12.5K] · Answer 1 · 2026-02-23T05:56:13+03:00

Answer:

The time required for the object to travel 74 feet is:

$t=2\ seconds$

The distance covered by a falling object in time t is described by the equation:

$d=5t+16t^2$

Now, we wish to calculate the time t necessary for the object to move 74 feet.

In other words, we need to determine t when d=74 ft.

That is:

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

Any quadratic equation of the form:

$ax^2+bx+c=0$

can be resolved using the quadratic formula:

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

In our scenario:

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

Now, substituting these values into the formula gives us:

$t=-2.313\ and\ t=2$

Since the time cannot be negative.

Thus, we conclude:

$t=2$

zzz [12.3K] · Answer 2 · 2026-02-23T05:56:47+03:00

zzz [12.3K]3 months ago

8 0

It is provided that

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

We need to determine t when d equals 74

Thus, $74=5t+16t^{2}$ 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 cannot be negative.

Thus, t equals 2

Therefore, it will require 2 seconds for the object to cover 74 feet.