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?
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1 point
Captionless Image
2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds

Answer 1

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**.