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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 [tex]h(t) = -16t^2 + 80t + 224[/tex], where [tex]t[/tex] represents the time in seconds that the baseball has been in the air and [tex]h(t)[/tex] represents the baseball's height in feet. When factored, this equation is [tex]h(t) = -16(t-7)(t+2)[/tex].

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

A. 7 seconds
B. 2 seconds
C. 9 seconds
D. 5 seconds

Sagot :

GinnyAnsweridn
To find how long it takes for the baseball to land on the ground, we need to solve the quadratic equation for when the height [tex]\( h(t) \)[/tex] is 0. The quadratic equation given is already factored for us:

[tex]\[ h(t) = -16(t-7)(t+2) \][/tex]

We solve for when [tex]\( h(t) = 0 \)[/tex]:

[tex]\[ -16(t-7)(t+2) = 0 \][/tex]

This equation is zero when either [tex]\( (t-7) = 0 \)[/tex] or [tex]\( (t+2) = 0 \)[/tex]. Thus, we set each factor equal to zero and solve for [tex]\( t \)[/tex]:

1. [tex]\( t-7 = 0 \)[/tex]

[tex]\[ t = 7 \][/tex]

2. [tex]\( t+2 = 0 \)[/tex]

[tex]\[ t = -2 \][/tex]

In the context of this problem, [tex]\( t \)[/tex] represents time, and time cannot be negative. Therefore, we discard [tex]\( t = -2 \)[/tex]. The only reasonable solution is [tex]\( t = 7 \)[/tex] seconds.

Therefore, the reasonable time for the baseball to land on the ground is:

[tex]\[ \boxed{7} \][/tex]

Thus, the correct answer is:
A. 7 seconds
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