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

Question

h = -16t ^2 + 320

Answer 1

To determine how long it will take for the rock to reach the river, we need to find the time \( t \) when the height \( h \) is equal to 0 (which corresponds to the rock reaching the river). The equation given is:

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

Setting \( h = 0 \):

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

Now, we can solve for \( t \):

1. Move 320 to the other side:

\[ 16t^2 = 320 \]

2. Divide both sides by 16:

\[ t^2 = 20 \]

3. Take the square root of both sides:

\[ t = \sqrt{20} \]

4. Simplifying the square root:

\[ t = \sqrt{4 \cdot 5} = 2\sqrt{5} \]

5. Calculating the numerical value (approximation):

Using \(\sqrt{5} \approx 2.236\):

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

Thus, the rock will take approximately 4.47 seconds to reach the river.