# Maximum Height of a Projectile Calculator

## About Maximum Height of a Projectile Calculator (Formula)

A Maximum Height of a Projectile Calculator is a tool used to determine the maximum vertical height reached by an object launched into the air under the influence of gravity. This calculator is particularly relevant in physics and engineering to analyze the motion of projectiles, such as thrown objects or projectiles launched from devices like catapults or rockets.

The formula for calculating the maximum height of a projectile is based on the kinematic equations of motion:

Maximum Height (h) = (v₀² * sin²(θ)) / (2 * g)

Where:

• Maximum Height (h) is the vertical distance above the launch point reached by the projectile.
• v₀ is the initial velocity of the projectile.
• θ is the launch angle of the projectile with respect to the horizontal.
• g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth).

To use the Maximum Height of a Projectile Calculator formula, follow these steps:

1. Determine the initial velocity (v₀) of the projectile, which is the speed at which it’s launched.
2. Determine the launch angle (θ) at which the projectile is launched. Ensure the angle is measured in radians if using trigonometric functions.
3. Plug the values of initial velocity (v₀) and launch angle (θ) into the formula: Maximum Height (h) = (v₀² * sin²(θ)) / (2 * g).
4. Calculate the maximum height (h) reached by the projectile.

The maximum height of a projectile occurs when its vertical velocity component becomes zero, meaning that the object momentarily stops ascending before reversing its motion and descending back to the ground.

This calculator is useful for various applications, including understanding the trajectory of projectiles, optimizing launch angles for maximum height, and predicting the motion of objects under the influence of gravity.