Question

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?

-2 seconds

-9 seconds

-5 seconds

-7 seconds

Answer 1

h(t) = 0 for t = 7 and for t = -2.

It is reasonable for the time to be positive, 7 seconds.

(The offered answers all appear to be negative, so none are reasonable.)

Answer 2

Answer:

7 seconds

Step-by-step explanation:

Given :

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 $h(t) = -16t^2 + 80t + 224$

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

Solution:

Equation : $h(t) = -16t^2 + 80t + 224$

When factored this equation : $h(t) = -16(t - 7)(t + 2)$  --A

Now we are supposed to find  reasonable time for it to take the baseball to land on the ground i.e. h =0

So, substitute h = 0 in A

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

$t=7,-2$

Since time cannot be negative

So, neglect -2

Thus it will taker 7 seconds for baseball to reach the ground.