Maximum Horizontal Range of a Projectile:

The maximum horizontal range of a projectile refers to the furthest distance the object can travel horizontally before hitting the ground. It is determined by the initial velocity, launch angle, and acceleration due to gravity.

Determining the Maximum Height:

To calculate the maximum height attained by a projectile, we need to consider the projectile's trajectory. The projectile follows a parabolic path, reaching its maximum height at the highest point of the trajectory before falling back to the ground.

Factors Affecting Maximum Height:

Several factors affect the maximum height attained by a projectile:

1. Initial Velocity: The greater the initial velocity, the higher the projectile will go before falling back down. However, keep in mind that the launch angle also plays a role.

2. Launch Angle: The launch angle is the angle at which the projectile is launched. The maximum height is achieved when the launch angle is 90 degrees (vertical launch). As the launch angle decreases, the maximum height decreases as well.

3. Acceleration due to Gravity: The acceleration due to gravity determines how quickly the projectile falls back to the ground. It is constant and equal to approximately 9.8 m/s² on Earth. The higher the acceleration due to gravity, the faster the projectile will fall, resulting in a lower maximum height.

Relationship between Maximum Range and Maximum Height:

The maximum range and maximum height of a projectile are related. When the maximum range is achieved, the projectile has covered the longest horizontal distance possible. At this point, the projectile is also at its highest point in the trajectory, which corresponds to the maximum height.

Conclusion:

In summary, the maximum height attained by a projectile depends on factors such as initial velocity, launch angle, and acceleration due to gravity. The maximum height is reached when the projectile is at its highest point in the trajectory. The relationship between the maximum range and maximum height is that they occur simultaneously.

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