Question
h(t)= -16t^2+40 is representive where t is time in seconds and h is height in feet where an egg protection contraption by dropping them off the roof of the school
Which point represents the height of the school roof
What is the height of the egg at t = 0.5 second. The height of the egg at 0.5 seconds is ____ feet
What is the height of the egg at 1 second
When does the egg hit the ground
Which point represents the height of the school roof
What is the height of the egg at t = 0.5 second. The height of the egg at 0.5 seconds is ____ feet
What is the height of the egg at 1 second
When does the egg hit the ground
Answers
GPT-4o mini
To analyze the height of the egg represented by the function \( h(t) = -16t^2 + 40 \), we can answer your questions step by step.
1. **Which point represents the height of the school roof?**
The height of the school roof corresponds to the height of the egg at time \( t = 0 \) seconds, which is when the egg is released from the roof.
\[
h(0) = -16(0)^2 + 40 = 40 \text{ feet}
\]
Thus, the height of the school roof is **40 feet**.
2. **What is the height of the egg at \( t = 0.5 \) seconds?**
Now, we will find the height when \( t = 0.5 \):
\[
h(0.5) = -16(0.5)^2 + 40
\]
\[
h(0.5) = -16(0.25) + 40
\]
\[
h(0.5) = -4 + 40 = 36 \text{ feet}
\]
The height of the egg at \( t = 0.5 \) seconds is **36 feet**.
3. **What is the height of the egg at \( t = 1 \) second?**
Next, we calculate the height at \( t = 1 \):
\[
h(1) = -16(1)^2 + 40
\]
\[
h(1) = -16 + 40 = 24 \text{ feet}
\]
The height of the egg at \( t = 1 \) second is **24 feet**.
4. **When does the egg hit the ground?**
The egg hits the ground when the height \( h(t) = 0 \). We can set the equation to zero and solve for \( t \):
\[
-16t^2 + 40 = 0
\]
\[
16t^2 = 40
\]
\[
t^2 = \frac{40}{16} = 2.5
\]
\[
t = \sqrt{2.5} \approx 1.58 \text{ seconds}
\]
Therefore, the egg hits the ground at approximately **1.58 seconds**.
In summary:
- The height of the school roof is **40 feet**.
- The height of the egg at \( t = 0.5 \) seconds is **36 feet**.
- The height of the egg at \( t = 1 \) second is **24 feet**.
- The egg hits the ground at approximately **1.58 seconds**.
1. **Which point represents the height of the school roof?**
The height of the school roof corresponds to the height of the egg at time \( t = 0 \) seconds, which is when the egg is released from the roof.
\[
h(0) = -16(0)^2 + 40 = 40 \text{ feet}
\]
Thus, the height of the school roof is **40 feet**.
2. **What is the height of the egg at \( t = 0.5 \) seconds?**
Now, we will find the height when \( t = 0.5 \):
\[
h(0.5) = -16(0.5)^2 + 40
\]
\[
h(0.5) = -16(0.25) + 40
\]
\[
h(0.5) = -4 + 40 = 36 \text{ feet}
\]
The height of the egg at \( t = 0.5 \) seconds is **36 feet**.
3. **What is the height of the egg at \( t = 1 \) second?**
Next, we calculate the height at \( t = 1 \):
\[
h(1) = -16(1)^2 + 40
\]
\[
h(1) = -16 + 40 = 24 \text{ feet}
\]
The height of the egg at \( t = 1 \) second is **24 feet**.
4. **When does the egg hit the ground?**
The egg hits the ground when the height \( h(t) = 0 \). We can set the equation to zero and solve for \( t \):
\[
-16t^2 + 40 = 0
\]
\[
16t^2 = 40
\]
\[
t^2 = \frac{40}{16} = 2.5
\]
\[
t = \sqrt{2.5} \approx 1.58 \text{ seconds}
\]
Therefore, the egg hits the ground at approximately **1.58 seconds**.
In summary:
- The height of the school roof is **40 feet**.
- The height of the egg at \( t = 0.5 \) seconds is **36 feet**.
- The height of the egg at \( t = 1 \) second is **24 feet**.
- The egg hits the ground at approximately **1.58 seconds**.