The maximum height of a projectile is calculated with the equation h = vy^2/2g, where g is the gravitational acceleration on Earth, 9.81 meters per second, h is the maximum height and vy is the vertical component of the projectile's velocity. If the angle of launch or the velocity of the projectile are not known, these quantities can be derived.
- Derive the original velocity and angle if not given these quantities
If the angle of launch and original velocity are not known, they can be derived from other information. To find the angle of launch from a given range and original velocity, use the equation 2(theta) = sin-1(gR/v^2), where theta is the angle and R is the range. Conversely, if the range and angle are known, take the square root of gR/sin2(theta). Unless a slide ruler is handy, a scientific calculator is necessary to find the sines of angles.
- Determine the vertical velocity of the projectile
As an example, assume a football has been thrown at an angle of 35 degrees at a velocity of 30 meters per second. To find the vertical velocity, multiply 30 by the sine of 35. This yields a vertical velocity of 17.21 meters per second.
- Plug this value into the height equation
Put this velocity into the height equation to get 17.21^2/19.62. Solving this yields the maximum height of 15.096 meters.