A juggler keeps on moving four balls in the air throwing the balls after regular intervals. When one ball leaves his hand `("speed" = 20 ms^-1)` the positions of other balls (height in m) `("Take" g = 10 ms^-2)`.

Options

A. ` 10, 20, 10`
B. ` 15, 20, 15`
C. ` 4, 15, 20`
D. ` 5, 10, 20`

Explanation

To solve the problem, we need to determine the heights of the three balls in the air when the fourth ball is thrown by the juggler. The initial speed of the balls is given as \( u = 20 \, \text{m/s} \) and the acceleration due to gravity is \( g = 10 \, \text{m/s}^2 \).

### Step-by-Step Solution:

1. **Calculate the total time for one ball to return to the juggler's hand**:
The time taken for a ball to reach the maximum height and then return to the juggler's hand is given by the formula:
\[ T = \frac{2u}{g} \]
Substituting the values:
\[ T = \frac{2 \times 20}{10} = 4 \, \text{seconds} \]

2. **Determine the time intervals for the balls**:
Since the juggler throws the balls at regular intervals and it takes 4 seconds for one ball to return, the time interval between each ball thrown is:
\[ \text{Interval} = \frac{T}{4} = 1 \, \text{second} \]

3. **Calculate the height of each ball at the moment the fourth ball is thrown**:
- **For Ball 1** (thrown 3 seconds ago):
\[ h_1 = ut - \frac{1}{2}gt^2 \]
where \( t = 3 \, \text{seconds} \):
\[ h_1 = 20 \times 3 - \frac{1}{2} \times 10 \times (3^2) = 60 - 45 = 15 \, \text{meters} \]

- **For Ball 2** (thrown 2 seconds ago):
\[ h_2 = ut - \frac{1}{2}gt^2 \]
where \( t = 2 \, \text{seconds} \):
\[ h_2 = 20 \times 2 - \frac{1}{2} \times 10 \times (2^2) = 40 - 20 = 20 \, \text{meters} \]

- **For Ball 3** (thrown 1 second ago):
\[ h_3 = ut - \frac{1}{2}gt^2 \]
where \( t = 1 \, \text{second} \):
\[ h_3 = 20 \times 1 - \frac{1}{2} \times 10 \times (1^2) = 20 - 5 = 15 \, \text{meters} \]

4. **Summarize the heights of the balls**:
- Height of Ball 1: \( 15 \, \text{meters} \)
- Height of Ball 2: \( 20 \, \text{meters} \)
- Height of Ball 3: \( 15 \, \text{meters} \)

Thus, the heights of the balls when the fourth ball is thrown are \( 15 \, \text{m}, 20 \, \text{m}, 15 \, \text{m} \).

### Final Answer:
The heights of the balls are \( 15 \, \text{m}, 20 \, \text{m}, 15 \, \text{m} \).

---