The maximum vertical heght to which a man can throw a ball is 136 m. The maximun horizontal distance upto which he can throw the same ball is

Options

A. 68 m
B. 136 m
C. 192 m
D. 272 m

Answer

To solve the problem, we need to find the maximum horizontal distance (R_max) a man can throw a ball, given the maximum vertical height (H_max) is 136 meters.

### Step-by-Step Solution:

1. **Understand the relationship between maximum height and maximum range**:
- The maximum height (H_max) achieved by a projectile is given by the formula:
\[ H_{max} = \frac{U^2}{2g} \]
where \( U \) is the initial velocity and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)).
- The maximum horizontal range (R_max) is given by the formula:
\[ R_{max} = \frac{U^2}{g} \]

2. **Relate R_max to H_max**:
- From the two equations, we can see that:
\[ R_{max} = 2 \times H_{max} \]
- This means that the maximum horizontal distance is double the maximum vertical height.

3. **Substitute the given height into the equation**:
- Given \( H_{max} = 136 \, m \):
\[ R_{max} = 2 \times 136 \, m = 272 \, m \]

4. **Final Answer**:
- Therefore, the maximum horizontal distance (R_max) that the man can throw the ball is:
\[ R_{max} = 272 \, m \]

### Conclusion:
The maximum horizontal distance up to which the man can throw the ball is **272 meters**.