A man throws balls with the same speed vertically upwards one after the other at an interval of 2s. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given `g = 9.8 m//s^(2)`)

Options

A. Any speed less than 19.6 m/s
B. Only with speed 19.6 m/s
C. More than 19.6 m/s
D. At least 9.8 m/s

Explanation

To solve the problem, we need to determine the speed at which a man should throw balls vertically upwards so that more than two balls are in the sky at any time. The key points to consider are the time interval between throws and the motion of the balls.

### Step-by-Step Solution:

1. **Understanding the Motion of the Balls**:
- When a ball is thrown upwards, it will rise until it reaches its maximum height, where its velocity becomes zero before it starts descending.
- The time taken to reach the maximum height can be calculated using the formula:
\[ t = \frac{u}{g} \]
where \( u \) is the initial velocity (speed of throw) and \( g \) is the acceleration due to gravity (9.8 m/s²).

2. **Total Time of Flight**:
- The total time of flight for the ball (time to go up and come back down) is given by:
\[ T = 2 \times \frac{u}{g} \]
This accounts for both the ascent and descent of the ball.

3. **Interval Between Throws**:
- The man throws a ball every 2 seconds. For more than two balls to be in the air at the same time, the time of flight \( T \) must be greater than the time interval between throws.

4. **Setting Up the Inequality**:
- To ensure that more than two balls are in the air at any time, we need:
\[ T > 2 \text{ seconds} \]
Substituting for \( T \):
\[ 2 \times \frac{u}{g} > 2 \]

5. **Solving for \( u \)**:
- Dividing both sides of the inequality by 2:
\[ \frac{u}{g} > 1 \]
- Multiplying both sides by \( g \):
\[ u > g \]
- Substituting \( g = 9.8 \, \text{m/s}^2 \):
\[ u > 9.8 \, \text{m/s} \]

6. **Conclusion**:
- Therefore, the speed of the throw must be greater than 9.8 m/s for more than two balls to be in the air simultaneously.

### Final Answer:
The speed of the throw should be greater than **9.8 m/s**.