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This problem involves calculating the free fall time and final speed of objects dropped in the Zero Gravity Research Facility, based on the given dataThis problem involves calculating the free fall time and final speed of objects dropped in the Zero Gravity Research Facility, based on the given 

- **Height of free fall**: 432 feet (132 meters)
- **Objects are dropped from rest**

We'll use the basic equations of motion for free fall under gravity:

1. **Time of fall**:
   The formula to calculate the time \( t \) for an object falling from rest is:
   \[
   t = \sqrt{\frac{2h}{g}}
   \]
   where:
   - \( h \) is the height (432 feet or 132 meters)
   - \( g \) is the acceleration due to gravity (32.2 ft/s² or 9.8 m/s²)

2. **Final speed**:
   The final speed \( v \) before braking can be calculated using:
   \[
   v = \sqrt{2gh}
   \]
   where the terms are the same as above.

Let me calculate both time and speed.For the objects falling from rest in the Zero Gravity Research Facility:

a. The falling time is approximately **5.18 seconds**.

b. The final speed before braking begins is about **166.80 feet per second**.

Would you like more details or have any questions? 

Here are five related questions to deepen your understanding:

1. How would the time of fall change if the height were doubled?
2. What would be the time of fall in meters if the height was measured in the metric system?
3. How does air resistance affect the calculations in real-world free-fall scenarios?
4. Could you apply the same equations on other planets with different gravity values?
5. How does the final speed relate to the kinetic energy of the object before braking?

**Tip:** For problems involving free fall, assuming no air resistance simplifies calculations, but in real-life conditions, drag could significantly affect the outcome.

Determine the falling time and final speed for objects dropped from rest in a 432-foot free fall at the NASA Zero Gravity Research Facility.

Learn how to calculate the time of fall and final speed for objects dropped from rest in a 432-foot free fall at NASA's Zero Gravity Research Facility. This problem covers kinematics and free fall equations, with key formulas for motion under gravity. Suitable for high school students.

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