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
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds

1 answer

To find how long it will take for the rock to reach the river, we can set the height \( h \) to 0 in the given equation:

\[ h = -16t^2 + 320 \]

Setting \( h = 0 \):

\[ 0 = -16t^2 + 320 \]

Rearranging the equation:

\[ 16t^2 = 320 \]

Dividing both sides by 16:

\[ t^2 = 20 \]

Taking the square root of both sides:

\[ t = \sqrt{20} \] \[ t = \sqrt{4 \times 5} = 2\sqrt{5} \]

Calculating \( \sqrt{5} \) gives approximately 2.236, so:

\[ t \approx 2 \times 2.236 \approx 4.472 \]

Therefore, the time \( t \) it will take for the rock to reach the river is approximately 4.5 seconds.

Thus, the answer is:

4.5 seconds.