Question

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Answer 1

Answer:

$t= 6\ s$

Step-by-step explanation:

We know that the equation that models the height of the ball as a function of time is $h(t) = -16t ^ 2 + 80t + 96$.

Where the initial speed is 80 feet.

When the ball lands on the ground, its height will be $h(t) = 0$.

So to know how long it will take the ball to reach the ground, equal h (t) to zero and solve for t.

$-16t ^ 2 + 80t + 96 = 0$

To solve this quadratic equation we use the quadratic formula.

For an equation of the form:

$at^2 +bt +c$

The quadratic formula is:

$t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}$

In this case

$a =-16\\b = 80\\c =96$

Then

$t=\frac{-80\±\sqrt{80^2 -4(-16)(96)}}{2(-16)}$

$t_1=-1\\\\t_2=6$

We take the positive solution

$t= 6\ s$

Answer 2

Answer:

After 5 seconds

Step-by-step explanation:

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