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 follow these steps:

### Step 1: Understand the Motion of the Balls
When the balls are dropped, they undergo free fall under the influence of gravity. The distance fallen by an object in free fall can be calculated using the formula:
\[ d = ut + \frac{1}{2}gt^2 \]
where:
- \( d \) is the distance fallen,
- \( u \) is the initial velocity (which is 0 for dropped balls),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.

### Step 2: Calculate the Time for Each Ball
- The 3rd ball is dropped 3 seconds before the 6th ball.
- The 4th ball is dropped 2 seconds before the 6th ball.
- The 5th ball is dropped 1 second before the 6th ball.

### Step 3: Calculate the Distances Fallen
1. **For the 3rd Ball:**
- Time \( t = 3 \) seconds
- Using the formula:
\[ d_3 = 0 \cdot 3 + \frac{1}{2} \cdot g \cdot (3^2) = \frac{1}{2} \cdot 9.8 \cdot 9 = 44.1 \, \text{meters} \]

2. **For the 4th Ball:**
- Time \( t = 2 \) seconds
- Using the formula:
\[ d_4 = 0 \cdot 2 + \frac{1}{2} \cdot g \cdot (2^2) = \frac{1}{2} \cdot 9.8 \cdot 4 = 19.6 \, \text{meters} \]

3. **For the 5th Ball:**
- Time \( t = 1 \) second
- Using the formula:
\[ d_5 = 0 \cdot 1 + \frac{1}{2} \cdot g \cdot (1^2) = \frac{1}{2} \cdot 9.8 \cdot 1 = 4.9 \, \text{meters} \]

### Step 4: Determine the Positions of the Balls
- The position of each ball from the top of the building when the 6th ball is being dropped:
- **3rd Ball:** 44.1 meters below the top of the building.
- **4th Ball:** 19.6 meters below the top of the building.
- **5th Ball:** 4.9 meters below the top of the building.

### Final Answer
- **Position of the 3rd Ball:** 44.1 meters
- **Position of the 4th Ball:** 19.6 meters
- **Position of the 5th Ball:** 4.9 meters

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