Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Question 46 A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equat...Question
A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation below. How long will it take the rock to reach the river
h = -16t ^2 + 320
h = -16t ^2 + 320
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine how long it will take for the rock to reach the river, we need to find the time \( t \) when the height \( h \) is equal to 0 (which corresponds to the rock reaching the river). The equation given is:
\[
h = -16t^2 + 320
\]
Setting \( h = 0 \):
\[
0 = -16t^2 + 320
\]
Now, we can solve for \( t \):
1. **Move 320 to the other side:**
\[
16t^2 = 320
\]
2. **Divide both sides by 16:**
\[
t^2 = 20
\]
3. **Take the square root of both sides:**
\[
t = \sqrt{20}
\]
4. **Simplifying the square root:**
\[
t = \sqrt{4 \cdot 5} = 2\sqrt{5}
\]
5. **Calculating the numerical value (approximation):**
Using \(\sqrt{5} \approx 2.236\):
\[
t \approx 2 \times 2.236 \approx 4.472
\]
Thus, the rock will take approximately **4.47 seconds** to reach the river.
\[
h = -16t^2 + 320
\]
Setting \( h = 0 \):
\[
0 = -16t^2 + 320
\]
Now, we can solve for \( t \):
1. **Move 320 to the other side:**
\[
16t^2 = 320
\]
2. **Divide both sides by 16:**
\[
t^2 = 20
\]
3. **Take the square root of both sides:**
\[
t = \sqrt{20}
\]
4. **Simplifying the square root:**
\[
t = \sqrt{4 \cdot 5} = 2\sqrt{5}
\]
5. **Calculating the numerical value (approximation):**
Using \(\sqrt{5} \approx 2.236\):
\[
t \approx 2 \times 2.236 \approx 4.472
\]
Thus, the rock will take approximately **4.47 seconds** to reach the river.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.