30. TOWER OF PISA: To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second, and 80 feet in the third second, regardless of its weight.

(1) (ii) How many feet would an object fall in the sixth second? How many feet would an object fall in the six second?

(iii) How many feet would an object fall in the eight second?

The problem describes how the distance an object falls increases as time progresses, following a constant acceleration due to gravity. From the given dataThe problem describes how the distance an object falls increases as time progresses, following a constant acceleration due to gravity. From the given 

- In the first second, the object falls 16 feet.
- In the second second, it falls 48 feet.
- In the third second, it falls 80 feet.

Notice the difference between each second is 32 feet, indicating a linear pattern of acceleration.

### (ii) How many feet would an object fall in the sixth second?

From the pattern:
- 1st second: 16 feet
- 2nd second: 48 feet
- 3rd second: 80 feet
- 4th second: \(80 + 32 = 112\) feet
- 5th second: \(112 + 32 = 144\) feet
- 6th second: \(144 + 32 = 176\) feet

Thus, in the sixth second, the object falls **176 feet**.

### (iii) How many feet would an object fall in the eighth second?

Continuing the pattern:
- 6th second: 176 feet
- 7th second: \(176 + 32 = 208\) feet
- 8th second: \(208 + 32 = 240\) feet

Thus, in the eighth second, the object falls **240 feet**.

Would you like more details on this calculation or have any further questions?

Here are 5 related questions to explore further:
1. How can we generalize the distance an object falls in any given second?
2. What is the total distance fallen after 8 seconds?
3. How does gravity affect the speed and acceleration of a falling object?
4. What mathematical formula represents the distance fallen after \(n\) seconds?
5. Can air resistance significantly affect the distance fallen?

**Tip:** The distance an object falls due to gravity increases quadratically over time because of constant acceleration.

30. TOWER OF PISA: To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second, and 80 feet in the third second, regardless of its weight. (1) (ii) How many feet would an object fall in the sixth second? (iii) How many feet would an object fall in the eighth second?

Understand how to calculate the distance an object falls in the sixth and eighth seconds using linear progression and constant acceleration. This problem includes Galileo's experiments, exploring how an object falls 176 feet in the sixth second and 240 feet in the eighth second. Suitable for students in Grades 8-10.

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