The maximum height reached by a projectile depends primarily on the initial vertical component of its velocity (which is influenced by the initial speed and the launch angle). It is also affected by the initial launch height and the acceleration due to gravity. The horizontal component of the velocity does not affect the maximum height. Specifically, the maximum height hmax⁡h_{\max}hmax​ can be calculated by the formula:

hmax⁡=h0+v02sin⁡2(θ)2gh_{\max}=h_0+\frac{v_0^2\sin^2(\theta)}{2g}hmax​=h0​+2gv02​sin2(θ)​

where:

• h0h_0h0​ is the initial height from which the projectile is launched,
• v0v_0v0​ is the initial velocity,
• θ\theta θ is the launch angle relative to the horizontal,
• ggg is the acceleration due to gravity.

At the maximum height, the vertical velocity component becomes zero because the projectile momentarily stops rising before beginning to fall back down.