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
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.