Question

Will give brainliest
A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2).


What is a reasonable time for it to take the baseball to land on the ground?


A. 2 seconds

B. 7 seconds

C. 9 seconds

D. 5 seconds

Answer 1

Answer:

B. 7 seconds

Step-by-step explanation:

Given:

$h(t) = -16(t-7)(t+2)$

Where $h(t)$ ⇒ height of the baseball in feet

$t$ ⇒ time in seconds that base ball has been in air

Solution:

Now we can say that;

When the base ball reaches the ground the base ball height will be become zero.

Hence $h(t) =0$

Now we will substitute in in equation we get;

$0= -16(t-7)(t+2)$

Dividing both side by -16 we get;

$\frac{0}{-16}=\frac{-16}{-16}(t-7)(t+2)\\\\0=(t-7)(t+2)$

Now we will find 2 values of t by substituting each with 0.

$t-7 =0\\\\t=7\\\\Or\\\\t+2=0\\\\t=-2$

Now we get the value of t as positive and negative and we know that time cannot be negative.

So we will discard the negative value of 't'.

Hence we can say that Baseball will reach the ground in 7 seconds.