If I drop a watermelon from the top of one of the tower dorms at CSU, and it takes 3.34 seconds to hit the ground, calculate how tall the building is in meters. 

To calculate the height of the building, we can use the equation for the displacement of an object in free fall under gravity:

\[
h = \frac{1}{2} g t^2
\]

Where:
- \( h \) is the height of the building (in meters),
- \( g \) is the acceleration due to gravity (\( 9.81 \, \text{m/s}^2 \)),
- \( t \) is the time it takes for the watermelon to hit the ground (3.34 seconds).

Now, substituting the values:

\[
h = \frac{1}{2} \times 9.81 \times (3.34)^2
\]

Let's calculate this.

\[
h = 0.5 \times 9.81 \times 11.1556 = 54.72 \, \text{m}
\]

So, the building is approximately **54.72 meters tall**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What would happen if air resistance were considered in this calculation?
2. How would the time change if the object were dropped from a higher building?
3. What formula is used to calculate the velocity upon impact?
4. How high would the building be if the time to hit the ground were 5 seconds?
5. What is the difference in fall time between an object dropped from 10 meters vs. 50 meters?

**Tip:** Always check the units when calculating physical quantities to ensure consistency and accuracy.

If I drop a watermelon from the top of one of the tower dorms at CSU, and it takes 3.34 seconds to hit the ground, calculate how tall the building is in meters.

Learn how to calculate the height of a building by using the time of free fall and the formula h = (1/2) g t^2. This problem demonstrates key physics concepts, including gravity and kinematics, and is suitable for students in Grades 9-12. The calculated height for a fall time of 3.34 seconds is approximately 54.72 meters.

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