Enter the initial velocity and the angle of launch of an object in projectile motion (assuming no air resistance) to calculate the maximum height of the projectile.
Maximum Projectile Height Formula
The following formula describes the maximum height of an object in projectile motion. As noted before, this is without air resistance.
h = V₀² * sin(α)² / (2 * g)
- Where his the maximum height
- V is the initial velocity
- α is the launch angle
Projectile motion is the act of an object moving in a two dimensional plane with the x axis representing the surface of the earth. In projectile motion, there is both vertical and horizontal motion. However, only vertical motion effects the maximum height. Therefore as is shown in the equation above, the vertical velocity is calculated using the sin of the angle of launch and the overall velocity.
How to calculate maximum projectile height
- First, determine the initial velocity.
This is the total velocity of the object.
- Next, determine the angle of launch
This is the angle measured with respect to the x-axis.
- Calculate the maximum height.
Enter the total velocity and angle of launch into the formula h = V₀² * sin(α)² / (2 * g) to calculate the maximum height.
The max height of a projectile is the maximum y value an object achieves under projectile motion. This max value is only determined by the y component of velocity and the force of gravity.