Question
At baseball practice, Matt hit the ball into the outfield. The function h(t)=−16t2+32t+3h(t)=−16t2+32t+3 gives the height h(t)h(t) of the baseball in feet, tt seconds after it is hit. A) What is the value of h(1)h(1)? Response area B) What does h(1.74)h(1.74) represent in context? Response area C) Which value would not be valid in the context of this problem? Response area The height of the ball 1 second after it is hit.The amount of time it takes for the ball to hit the ground.3The height of the ball 1.74 seconds after it is hit.h(0)h(0)h(−2)h(−2)The time it took the ball to be 1.74 feet above the ground.2.1h(2)h(2)19
Answers
GPT-4o mini
Let's break down each part of the question based on the function \( h(t) = -16t^2 + 32t + 3 \).
**A) Calculate \( h(1) \)**
To find \( h(1) \), substitute \( t = 1 \) into the function:
\[
h(1) = -16(1)^2 + 32(1) + 3
\]
\[
h(1) = -16 + 32 + 3
\]
\[
h(1) = 16 + 3 = 19
\]
So the value of \( h(1) \) is **19 feet**.
---
**B) What does \( h(1.74) \) represent in context?**
The function \( h(t) \) gives the height of the baseball \( t \) seconds after it is hit. Therefore, \( h(1.74) \) represents the height of the baseball **1.74 seconds** after it is hit.
---
**C) Which value would not be valid in the context of this problem?**
1. The height of the ball 1 second after it is hit. (Valid, since we just calculated \( h(1) = 19 \))
2. The amount of time it takes for the ball to hit the ground. (This is valid but we need the actual value to confirm it's valid)
3. The height of the ball 1.74 seconds after it is hit. (Valid, as we mentioned above)
4. \( h(0) \) (Valid, as this gives the height at time zero)
5. \( h(-2) \) (Invalid, as negative time doesn't make sense in this context for height calculation)
6. The time it took the ball to be 1.74 feet above the ground. (In principle, this is valid depending on the specific context and calculations.)
Thus, the value that would **not** be valid in the context of this problem is **\( h(-2) \)**. Negative time does not exist in this context, as it cannot represent a time before the ball was hit.
**A) Calculate \( h(1) \)**
To find \( h(1) \), substitute \( t = 1 \) into the function:
\[
h(1) = -16(1)^2 + 32(1) + 3
\]
\[
h(1) = -16 + 32 + 3
\]
\[
h(1) = 16 + 3 = 19
\]
So the value of \( h(1) \) is **19 feet**.
---
**B) What does \( h(1.74) \) represent in context?**
The function \( h(t) \) gives the height of the baseball \( t \) seconds after it is hit. Therefore, \( h(1.74) \) represents the height of the baseball **1.74 seconds** after it is hit.
---
**C) Which value would not be valid in the context of this problem?**
1. The height of the ball 1 second after it is hit. (Valid, since we just calculated \( h(1) = 19 \))
2. The amount of time it takes for the ball to hit the ground. (This is valid but we need the actual value to confirm it's valid)
3. The height of the ball 1.74 seconds after it is hit. (Valid, as we mentioned above)
4. \( h(0) \) (Valid, as this gives the height at time zero)
5. \( h(-2) \) (Invalid, as negative time doesn't make sense in this context for height calculation)
6. The time it took the ball to be 1.74 feet above the ground. (In principle, this is valid depending on the specific context and calculations.)
Thus, the value that would **not** be valid in the context of this problem is **\( h(-2) \)**. Negative time does not exist in this context, as it cannot represent a time before the ball was hit.