A person sitting on the top of a tall building is dropping balls at regular intervals of one second. Find the positions of the 3rd, 4th and 5th ball when the 6th ball is being dropped.

Explanation

To solve the problem of finding the positions of the 3rd, 4th, and 5th balls when the 6th ball is being dropped, we can use the equations of motion under gravity.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A person drops balls from the top of a tall building at regular intervals of one second.
- We need to find the positions of the 3rd, 4th, and 5th balls at the moment the 6th ball is dropped.

2. **Identifying the Time Intervals**:
- When the 6th ball is dropped, the time intervals for the other balls are:
- 5th ball: 1 second before the 6th ball
- 4th ball: 2 seconds before the 6th ball
- 3rd ball: 3 seconds before the 6th ball

3. **Using the Equation of Motion**:
- The equation of motion under gravity is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
- Here, \( u = 0 \) (initial velocity), \( a = -g \) (acceleration due to gravity, negative because it is downward).
- Thus, the equation simplifies to:
\[ s = -\frac{1}{2} g t^2 \]

4. **Calculating the Position of the 5th Ball**:
- For the 5th ball (t = 1 second):
\[ s_5 = -\frac{1}{2} \times 9.81 \times (1)^2 = -4.9 \text{ meters} \]

5. **Calculating the Position of the 4th Ball**:
- For the 4th ball (t = 2 seconds):
\[ s_4 = -\frac{1}{2} \times 9.81 \times (2)^2 = -19.6 \text{ meters} \]

6. **Calculating the Position of the 3rd Ball**:
- For the 3rd ball (t = 3 seconds):
\[ s_3 = -\frac{1}{2} \times 9.81 \times (3)^2 = -44.1 \text{ meters} \]

7. **Final Positions**:
- The positions of the balls when the 6th ball is being dropped are:
- 5th ball: -4.9 meters
- 4th ball: -19.6 meters
- 3rd ball: -44.1 meters

### Summary of Positions:
- 3rd ball: -44.1 meters
- 4th ball: -19.6 meters
- 5th ball: -4.9 meters