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. Only with speed `19.6 m s^(-1)`
B. More than `19.6 m s^(-1)`
C. At least `9.8 m s^(-1)`
D. Any speed less than `19.6 m s^(-1)`

Answer

To solve the problem, we need to determine the minimum speed at which a man must throw balls vertically upwards so that more than two balls are in the air at the same time.

### Step-by-Step Solution:

1. **Understand the Problem**:
- A man throws balls vertically upwards at an interval of 2 seconds.
- We need to find the minimum speed (u) such that more than two balls are in the air at the same time.

2. **Use the Kinematic Equation**:
- When a ball is thrown upwards, it will rise until it reaches its maximum height, where its final velocity (v) becomes 0.
- The kinematic equation we can use is:
\[ v = u - gt \]
- Here, \( g \) is the acceleration due to gravity (9.8 m/s²), \( u \) is the initial speed, and \( t \) is the time taken to reach the maximum height.

3. **Determine Time to Reach Maximum Height**:
- At maximum height, \( v = 0 \). Therefore, we can set the equation to:
\[ 0 = u - gt \]
- Rearranging gives:
\[ u = gt \]

4. **Calculate Time to Reach Maximum Height**:
- The time taken to reach the maximum height (t) can be calculated as:
\[ t = \frac{u}{g} \]

5. **Find the Condition for More than Two Balls in the Air**:
- Since the balls are thrown every 2 seconds, we need to ensure that the time taken to reach the maximum height is greater than 2 seconds.
- Thus, we need:
\[ \frac{u}{g} > 2 \]

6. **Substituting the Value of g**:
- Substituting \( g = 9.8 \, \text{m/s}^2 \):
\[ \frac{u}{9.8} > 2 \]
- Multiplying both sides by 9.8 gives:
\[ u > 19.6 \, \text{m/s} \]

7. **Conclusion**:
- Therefore, the speed of the throw must be more than 19.6 m/s for more than two balls to be in the air at the same time.

### Final Answer:
The speed of the throw should be more than **19.6 m/s**.