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 \( t \):
- Rearranging the equation gives:
\[ 16t^2 = 320 \]
- Dividing both sides by 16:
\[ t^2 = 20 \]
- Taking the square root of both sides:
\[ t = \sqrt{20} \]
- 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.