Let's analyze the options given for the ordered pair [tex]\((2, 4.9)\)[/tex] in the context of the function [tex]\( h(t) = 24.5 - 4.9t^2 \)[/tex], which models the height [tex]\(h\)[/tex] of a water balloon in meters, [tex]\(t\)[/tex] seconds after it is dropped from a balcony.
First, we interpret the ordered pair [tex]\((2, 4.9)\)[/tex]:
- The first element in the ordered pair, [tex]\(2\)[/tex], represents the time [tex]\(t\)[/tex] in seconds.
- The second element in the ordered pair, [tex]\(4.9\)[/tex], represents the height [tex]\(h\)[/tex] in meters.
The given function provides the height [tex]\(h\)[/tex] as a function of time [tex]\(t\)[/tex].
### Step-by-Step Analysis:
1. Determine the height after 2 seconds:
- Substitute [tex]\(t = 2\)[/tex] into the function:
[tex]\[ h(2) = 24.5 - 4.9 \cdot 2^2 \][/tex]
2. Simplify the expression:
- First, calculate [tex]\(2^2\)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
- Then, multiply by 4.9:
[tex]\[ 4.9 \cdot 4 = 19.6 \][/tex]
- Finally, subtract this result from 24.5:
[tex]\[ 24.5 - 19.6 = 4.9 \][/tex]
Therefore, the height of the water balloon 2 seconds after it is dropped is 4.9 meters.
### Evaluate the Given Options:
- Option (A): The height of the water balloon is 4.9 meters 2 seconds after it is dropped.
- This directly matches our calculation and interpretation of the ordered pair [tex]\((2, 4.9)\)[/tex].
- Option (B): The height of the water balloon is 2 meters 4.9 seconds after it is dropped.
- This is incorrect because it misinterprets the values, suggesting 4.9 seconds instead of 2 seconds.
- Option (C): The water balloon travels 4.9 meters in 2 seconds.
- This is incorrect because it describes a distance traveled over time, rather than the height of the balloon after a specific time.
- Option (D): The water balloon travels 2 meters in 4.9 seconds.
- This is also incorrect because it misinterprets the values and the relationship between time and height.
### Conclusion:
The best interpretation of the ordered pair [tex]\((2, 4.9)\)[/tex] is given by:
[tex]\[
\boxed{A}
\][/tex]
Option (A) is correct – The height of the water balloon is 4.9 meters 2 seconds after it is dropped.
