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. How long will it take the rock to reach the river
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.