Question

A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football above the ground is given by s (t)=-16^2+50t+4, where t is time, in seconds, and t>=0. At what time will the football be 25 feet above the ground?
3.625 seconds
3.20 seconds
0.5 seconds or 3.625 seconds
0.5 seconds or 2.625 seconds

Answer 1

S(t) = -16t^2 + 50t + 4

This equation gives us relation between time and traveled distance. That means that if we put some time we can see how much distance ball will travel or oposite from that if we have some distance to travel we can calculate how much time will it require to do so.
Second case is actually what we need for our task.

25 = -16t^2 + 50t + 4
-16t^2 +50t - 21 = 0

Now we get 2 times which is obvious because ball will reach 25 feet when it is ascending and when it is descending.

t1 = 1/2
t2 = 2,625

Both are the answers.

Answer 2

Answer: 0.5 seconds or 2.625 seconds

Explanation:

At t = 0, The ball is 4 ft above the ground.

The height of the football varies with time in the following way:

s(t) = -16 t² + 50 t + 4

we need to find the time in which the height would of the football would be 25 ft:

⇒25 = -16 t² + 50 t + 4

we need to solve the quadratic equation:

⇒ 16 t² - 50 t + 21 = 0

$t = \frac{50 \pm \sqrt{50^2-4\times 16\times 21}}{2\times16}$

⇒ t = 0.5 s or 2.625 s

Therefore, at t = 0.5 s or 2.625 s, the football would be 25 ft above the ground.