# How do you calculate the maximum height of a projectile launched straight up?

## Question:

How do you calculate the maximum height of a projectile launched straight up?

## Straight motion in the vertical direction:

When the object is launched straight up, then the height of the object increases, which leads to an increase the potential energy of the object. At the maximum height, the velocity or the kinetic energy of the object becomes zero and the total energy is the potential energy.

When the object is launched, it has only kinetic energy and when it reaches the maximum height, then the only energy is the potential energy.

Therefore, taking energy conservation

{eq}\begin{align} \rm mgh &= \rm \dfrac{1}{2}mv^{2} \\ \rm h &= \rm \dfrac{v^{2}}{2g} \\ \end{align} {/eq}

where

• h is the maximum height
• v is the velocity
• g is the acceleration due to gravity
• m is the mass of the object