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 where. How long will it take the rock to reach the river
h = -16t^2 + 320
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds
h = -16t^2 + 320
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 find out how long it takes the rock to reach the river, we can set the height \( h \) of the rock to 0 (the height of the river) in the given equation:
\[
h = -16t^2 + 320
\]
Setting \( h = 0 \):
\[
0 = -16t^2 + 320
\]
Now, let's solve for \( t \):
1. Rearranging the equation gives:
\[
16t^2 = 320
\]
2. Dividing both sides by 16:
\[
t^2 = 20
\]
3. Taking the square root of both sides:
\[
t = \sqrt{20}
\]
4. Simplifying this gives:
\[
t = 4.47 \text{ seconds} \quad (\text{approximately})
\]
So, the time it takes for the rock to reach the river is approximately 4.5 seconds.
Among the options provided, the closest answer is **4.5 seconds**.
\[
h = -16t^2 + 320
\]
Setting \( h = 0 \):
\[
0 = -16t^2 + 320
\]
Now, let's solve for \( t \):
1. Rearranging the equation gives:
\[
16t^2 = 320
\]
2. Dividing both sides by 16:
\[
t^2 = 20
\]
3. Taking the square root of both sides:
\[
t = \sqrt{20}
\]
4. Simplifying this gives:
\[
t = 4.47 \text{ seconds} \quad (\text{approximately})
\]
So, the time it takes for the rock to reach the river is approximately 4.5 seconds.
Among the options provided, the closest answer is **4.5 seconds**.
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