To solve the problems, we will first evaluate \( h(2.5) \).
### a) Find \( h(2.5) \).
Using the given function:
\[
h(t) = -16t^2 + 80t + 30
\]
Substituting \( t = 2.5 \):
\[
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
\]
Calculating \( (2.5)^2 \):
\[
(2.5)^2 = 6.25
\]
So now we substitute:
\[
h(2.5) = -16(6.25) + 80(2.5) + 30
\]
Calculating \( -16(6.25) \):
\[
-16 \times 6.25 = -100
\]
Calculating \( 80(2.5) \):
\[
80 \times 2.5 = 200
\]
Putting it all together:
\[
h(2.5) = -100 + 200 + 30 = 130
\]
Thus,
\[
h(2.5) = 130
\]
### b) What does \( h(2.5) \) represent in the context of this problem?
In the context of this problem, \( h(2.5) \) represents **the height of the rock 2.5 seconds after it has been thrown.**
### c) Does it make sense to find \( h(-10) \) in the context of this problem?
No, it does not make sense because time cannot be negative.
### Summary of Answers:
- a) \( h(2.5) = 130 \)
- b) The height of the rock 2.5 seconds after it has been thrown.
- c) No, it does not make sense because time cannot be negative.