Question
A rock is droop from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h(t)=-16t^2+320. Approximately how long will it take the rock to reach the river
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine how long it takes for the rock to reach the river, we need to find the value of \( t \) when the height \( h(t) \) of the rock is 0 (i.e., when it reaches the river). The equation given is:
\[
h(t) = -16t^2 + 320
\]
To find when the rock hits the river, we set \( h(t) \) to 0:
\[
0 = -16t^2 + 320
\]
Now, let's solve for \( t \):
1. Rearrange the equation:
\[
16t^2 = 320
\]
2. Divide both sides by 16:
\[
t^2 = \frac{320}{16} = 20
\]
3. Take the square root of both sides:
\[
t = \sqrt{20} \approx 4.47 \text{ seconds}
\]
Therefore, the rock will take approximately **4.5 seconds** to reach the river.
\[
h(t) = -16t^2 + 320
\]
To find when the rock hits the river, we set \( h(t) \) to 0:
\[
0 = -16t^2 + 320
\]
Now, let's solve for \( t \):
1. Rearrange the equation:
\[
16t^2 = 320
\]
2. Divide both sides by 16:
\[
t^2 = \frac{320}{16} = 20
\]
3. Take the square root of both sides:
\[
t = \sqrt{20} \approx 4.47 \text{ seconds}
\]
Therefore, the rock will take approximately **4.5 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.