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

Question

h = -16t^2 + 320
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds

Answer 1

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.