how long would it take for a ball dropped from the top of a 400
-foot building to hit the ground? 

To find how long it will take for a ball to hit the ground when dropped from a height of 400 feet, we can use the formula for free fall under gravity:

\[
t = \sqrt{\frac{2h}{g}}
\]

Where:
- \( t \) is the time it takes to hit the ground.
- \( h \) is the height (400 feet).
- \( g \) is the acceleration due to gravity (approximately \( 32.2 \, \text{ft/s}^2 \)).

Now, let's calculate it:

\[
t = \sqrt{\frac{2 \times 400}{32.2}} \approx \sqrt{24.84} \approx 4.99 \, \text{seconds}
\]

So, it will take approximately **5 seconds** for the ball to hit the ground.

Would you like further details on this, or have any other questions?

Here are some related questions for you to explore:

1. What is the velocity of the ball just before hitting the ground?
2. How would the time change if the building were 800 feet tall?
3. What would happen if the ball were thrown downwards with an initial velocity?
4. How does air resistance affect the fall time of the ball?
5. Can you calculate the time taken if dropped on a planet with different gravity?

**Tip**: When dealing with free-fall problems, make sure to use consistent units for height and gravity!

How long would it take for a ball dropped from the top of a 400-foot building to hit the ground?

Learn how to calculate the time it takes for a ball dropped from a 400-foot building to hit the ground using the formula for free fall under gravity. This problem involves kinematics and the equation of motion. Suitable for students in Grades 9-12.

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