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
