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

7 seconds

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.

Answer 2

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.)