**Maximum Horizontal Distance vs Maximum Height**

When a cricketer throws a ball, the path of the ball can be divided into two components: the horizontal component and the vertical component. The maximum horizontal distance refers to the farthest point on the ground where the ball can land. However, the maximum height refers to the highest point the ball can reach above the ground.

**Factors Affecting Maximum Height**

Several factors affect the maximum height the ball can reach when thrown by a cricketer. These factors include the initial velocity, angle of projection, and gravitational force.

- **Initial Velocity**: The initial velocity of the ball determines how fast it leaves the cricketer's hand. A higher initial velocity will result in a greater maximum height.
- **Angle of Projection**: The angle at which the ball is thrown also affects its maximum height. A higher angle of projection will result in a greater maximum height.
- **Gravitational Force**: The force of gravity acts on the ball throughout its trajectory, causing it to eventually fall back to the ground. The longer the ball remains in the air, the higher it will go. However, the gravitational force limits the maximum height that can be achieved.

**Projectile Motion**

When a cricketer throws a ball, it follows a curved path known as projectile motion. This motion can be analyzed by breaking it into horizontal and vertical components.

- The horizontal component of the motion remains constant and is not affected by gravity. Therefore, the maximum horizontal distance remains the same regardless of the initial velocity or angle of projection.
- The vertical component of the motion is affected by gravity. As the ball moves upward, the gravitational force acts against it, slowing it down until it reaches its peak height. Then, the ball starts to fall back to the ground due to gravity.

**Calculating Maximum Height**

To calculate the maximum height, we need to consider the initial velocity, angle of projection, and gravitational force. By using the equations of motion and trigonometry, we can determine the maximum height reached by the ball.

- The initial vertical velocity can be calculated as V₀ * sin(θ), where V₀ is the initial velocity and θ is the angle of projection.
- The time taken for the ball to reach its peak height can be calculated using the equation T = (V₀ * sin(θ)) / g, where g is the acceleration due to gravity.
- The maximum height can be calculated using the equation H = (V₀ * sin(θ))² / (2 * g).

Using these calculations, we can determine the maximum height the ball can reach when thrown by a cricketer.

**Conclusion**

In conclusion, the cricketer can throw the ball to a maximum horizontal distance of 100m. However, the maximum height the ball can reach above the ground depends on various factors such as the initial velocity, angle of projection, and gravitational force. By analyzing the projectile motion and applying the equations of motion, the maximum height can be calculated. It is important to note that the maximum height achieved by the ball will be less than the maximum horizontal distance due to the influence of gravity.