The formula sequals=16tsquared2 is used to approximate the distance​ s, in​ feet, that an object falls freely from rest in t seconds. The height of a building is 13241324 feet. How long would it take for an object to fall from the​ top?

The formula provided for the distance \( s \) is \( s = 16t^2 \), where \( s \) is the distance in feet and \( t \) is the time in seconds.

You are given that the height of the building is 1324 feet. So, we can substitute \( s = 1324 \) into the equation and solve for \( t \).

\[
1324 = 16t^2
\]

To solve for \( t \), follow these steps:

1. Divide both sides by 16:
\[
t^2 = \frac{1324}{16}
\]
\[
t^2 = 82.75
\]

2. Take the square root of both sides to solve for \( t \):
\[
t = \sqrt{82.75}
\]
\[
t \approx 9.09 \, \text{seconds}
\]

So, it would take approximately 9.09 seconds for an object to fall from the top of the building.

Would you like more details or have any questions?

Here are 5 related questions you might be interested in:
1. What is the impact of air resistance on the time of fall?
2. How does the height of the building affect the time of fall?
3. What is the velocity of the object after it has fallen for 9 seconds?
4. How can we generalize this formula for different gravitational fields?
5. What is the maximum height from which an object can fall freely without air resistance?

**Tip:** For objects falling freely from rest, velocity increases linearly over time, but the distance fallen increases quadratically.

The formula s = 16t^2 is used to approximate the distance​ s, in​ feet, that an object falls freely from rest in t seconds. The height of a building is 1324 feet. How long would it take for an object to fall from the​ top?

Discover how to calculate the time for an object to fall from a 1324-ft tall building using the formula s = 16t^2. This problem involves key algebraic and kinematic concepts, focusing on solving quadratic equations. Suitable for students in Grades 8-10.

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