To determine how long it takes for a rock dropped from a height of 320 feet above a river to reach the river, we can use the equation of motion under constant acceleration due to gravity. The general equation for the distance fallen is:
\[ d = \frac{1}{2}gt^2 \]
where:
- \( d \) = distance fallen (in feet),
- \( g \) = acceleration due to gravity (approximately \( 32 , \text{ft/s}^2 \) on Earth),
- \( t \) = time in seconds.
In this case, the rock is dropped from a height of 320 feet, so we set \( d = 320 \) feet.
Substituting \( d \) into the equation gives us:
\[ 320 = \frac{1}{2} (32) t^2 \]
This simplifies to:
\[ 320 = 16t^2 \]
To solve for \( t^2 \), divide both sides by 16:
\[ t^2 = \frac{320}{16} \]
\[ t^2 = 20 \]
Now take the square root of both sides to find \( t \):
\[ t = \sqrt{20} \]
Calculating this gives:
\[ t = \sqrt{20} \approx 4.47 \text{ seconds} \]
Thus, the time it takes for the rock to reach the river is approximately 4.5 seconds.
So the correct answer is 4.5 seconds.
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