Question
At baseball practice, Matt hit the ball into the outfield. The function: h (t) = -16t^2 + 32t + 3, gives the height: h (t), of the baseball in feet: t, seconds after it is hit.
A.) What is the value of: h (1)
B.): What does: h (1.74) represent in context?
C.): Which value would not be valid in the context of this problem?
Options for all questions:
19, h (-2), the height of the ball 1 second after it is hit, the height of the ball 1.74 seconds after it is hit, 3, 2.1, h (2), the amount of time it takes for the ball to hit the ground, h (0), The time it took for the ball to be 1.74 feet above the ground.
A.) What is the value of: h (1)
B.): What does: h (1.74) represent in context?
C.): Which value would not be valid in the context of this problem?
Options for all questions:
19, h (-2), the height of the ball 1 second after it is hit, the height of the ball 1.74 seconds after it is hit, 3, 2.1, h (2), the amount of time it takes for the ball to hit the ground, h (0), The time it took for the ball to be 1.74 feet above the ground.
Answers
GPT-4o mini
Let's break down the problem step by step to answer each of the parts logically.
### A. What is the value of: h(1)?
To find \( h(1) \), we need to substitute \( t = 1 \) into the function \( h(t) = -16t^2 + 32t + 3 \).
\[
h(1) = -16(1^2) + 32(1) + 3
\]
\[
h(1) = -16(1) + 32 + 3
\]
\[
h(1) = -16 + 32 + 3
\]
\[
h(1) = 19
\]
**So, \( h(1) = 19 \).**
### B. What does: h(1.74) represent in context?
The value \( h(1.74) \) represents the height of the baseball at \( t = 1.74 \) seconds after it is hit.
**In context, it means the height of the ball 1.74 seconds after it is hit.**
### C. Which value would not be valid in the context of this problem?
We need to consider what values would be valid within the context of hitting a baseball. Here are the options:
1. **h(-2)**: This does not make sense in the context of time because you cannot go back in time – negative time does not have a physical meaning in this context.
2. **h(0)**: This represents the height of the ball at the moment it is hit, which is valid.
3. **The height of the ball 1 second after it is hit**: This is also valid (as calculated in part A).
4. **The height of the ball 1.74 seconds after it is hit**: This is valid (as discussed in part B).
5. **19**: This is a height value calculated and is valid.
6. **2.1**: There is no context provided for this value, but it could represent a possible height.
7. **h(2)**: This is valid and would represent the height of the ball 2 seconds after it is hit.
8. **The amount of time it takes for the ball to hit the ground**: This value is relevant as it’s a significant aspect of the ball’s trajectory.
9. **The time it took for the ball to be 1.74 feet above the ground**: This is invalid unless specifically solved through the function.
In conclusion, **h(-2)** would not be valid in the context of this problem since it implies a negative time, which cannot occur in this scenario.
### Summary of Answers
A. \( h(1) = 19 \)
B. \( h(1.74) \) represents the height of the ball 1.74 seconds after it is hit.
C. **h(-2)** is not valid in the context of this problem.
### A. What is the value of: h(1)?
To find \( h(1) \), we need to substitute \( t = 1 \) into the function \( h(t) = -16t^2 + 32t + 3 \).
\[
h(1) = -16(1^2) + 32(1) + 3
\]
\[
h(1) = -16(1) + 32 + 3
\]
\[
h(1) = -16 + 32 + 3
\]
\[
h(1) = 19
\]
**So, \( h(1) = 19 \).**
### B. What does: h(1.74) represent in context?
The value \( h(1.74) \) represents the height of the baseball at \( t = 1.74 \) seconds after it is hit.
**In context, it means the height of the ball 1.74 seconds after it is hit.**
### C. Which value would not be valid in the context of this problem?
We need to consider what values would be valid within the context of hitting a baseball. Here are the options:
1. **h(-2)**: This does not make sense in the context of time because you cannot go back in time – negative time does not have a physical meaning in this context.
2. **h(0)**: This represents the height of the ball at the moment it is hit, which is valid.
3. **The height of the ball 1 second after it is hit**: This is also valid (as calculated in part A).
4. **The height of the ball 1.74 seconds after it is hit**: This is valid (as discussed in part B).
5. **19**: This is a height value calculated and is valid.
6. **2.1**: There is no context provided for this value, but it could represent a possible height.
7. **h(2)**: This is valid and would represent the height of the ball 2 seconds after it is hit.
8. **The amount of time it takes for the ball to hit the ground**: This value is relevant as it’s a significant aspect of the ball’s trajectory.
9. **The time it took for the ball to be 1.74 feet above the ground**: This is invalid unless specifically solved through the function.
In conclusion, **h(-2)** would not be valid in the context of this problem since it implies a negative time, which cannot occur in this scenario.
### Summary of Answers
A. \( h(1) = 19 \)
B. \( h(1.74) \) represents the height of the ball 1.74 seconds after it is hit.
C. **h(-2)** is not valid in the context of this problem.