A juggler maintains four balls in motion, making each to them to rise a height of `20 m` from his hand. What time interval should he maintain, for the alphaer distance between them.

Options

A. `3s`
B. `3/2s`
C. `1s`
D. `2s`

Answer

To solve the problem of how much time interval a juggler should maintain between throwing four balls that rise to a height of 20 meters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Height (h) = 20 m
- Acceleration due to gravity (g) = 10 m/s² (approximately)

2. **Calculate the Initial Velocity (u)**:
We can use the kinematic equation:
\[ v^2 = u^2 + 2as \]
At the maximum height, the final velocity (v) is 0. Therefore, we can rearrange the equation to find the initial velocity (u):
\[ 0 = u^2 - 2gh \]
\[ u^2 = 2gh \]
Substituting the values:
\[ u^2 = 2 \times 10 \times 20 = 400 \]
\[ u = \sqrt{400} = 20 \text{ m/s} \]

3. **Calculate the Time to Reach Maximum Height (t_up)**:
We can use the equation:
\[ v = u + at \]
Rearranging to solve for time (t):
\[ 0 = 20 - 10t \]
\[ 10t = 20 \implies t = 2 \text{ seconds} \]
This is the time taken to reach the maximum height.

4. **Calculate the Total Time for the Ball to Go Up and Come Back Down (t_total)**:
The total time for the ball to go up and come back down is:
\[ t_{total} = t_{up} + t_{down} = 2 + 2 = 4 \text{ seconds} \]

5. **Determine the Time Interval Between Throws**:
Since the juggler is juggling four balls, he needs to throw each ball at intervals that allow all four balls to be in the air at the same time. To maintain this juggling pattern, he should throw a ball every second:
- Throw 1: t = 0s
- Throw 2: t = 1s
- Throw 3: t = 2s
- Throw 4: t = 3s

This means the juggler should maintain a time interval of **1 second** between each throw.

### Final Answer:
The juggler should maintain a time interval of **1 second** between throwing each ball.