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# Ballistic Max Height

vCalc.Ballistic Max Height

The **Maximum Ballistic Height** calculator compute maximum vertical altitude (**M _{h}**) above a plane that is reached by an object launched at an angle above the horizon (

**θ**) at an initial velocity (

**V**) assuming a constant downward acceleration (

**g**).

**INSTRUCTIONS**: Choose units and enter the following:

- (
**V**) This is the initial velocity. - (
**h**) This is the initial height above the plane. - (
**θ**) This is the angle above the horizon. - (
**g**) This is the acceleration due to gravity (default is 9.80665 m/s^{2})

**Max Altitude (M _{h})**: The calculator returns the maximum height achieved in meters. However this can be automatically converted to other length units via the pull-down menu.

#### Ballistic Flight Equations and Calculators:

- Ballistic Maximum Altitude: This is the maximum altitude achieved in free ballistic flight.
- Ballistic Maximum Range: This is the maximum horizontal range.
- Velocity to achieve a Max Ballistic Height: This computes the initial velocity required to achieve the max height.
- Ballistic Flight Time: This is the time duration of free flight.
- Ballistic Vertical Velocity: This is the vertical velocity at a given time.
- Ballistic Horizontal Velocity: This is horizontal velocity or ground speed.
- Vertical Position in Ballistic Flight: This compute the vertical position (y) at a given time within ballistic flight.
- Horizontal Position in Ballistic Flight: This compute the horizontal position (x) at a given time within ballistic flight.

#### The Math / Science

The **Max Ballistic Height** equation is used to compute the maximum height (**h**) of an object in trajectory motion above a plane. The range is based on negative vertical acceleration (**g**), initial velocity (**V**) and launch angle (θ). This simplified ballistic equation does not take into account any drag or other forces and this equation assumes the launch point (origin) is on the plane.

The formula for **Max Ballistic Height** is:

h = (V • sin(θ))² / (2•g)

- h is the maximum height.
- V the magnitude of the initial launch
**velocity to achieve a Max Ballistic Height** - θ is the launch angle (angle from the local horizontal plane)
- g is the acceleration due to gravity.

# Usage

Note: a default for gravitational acceleration (**g**) of 9.80665 meters per seconds squared is provided. This is the approximate SI value at sea level on earth. The user may change the gravitational acceleration constant (**g**) to accommodate a different body (e.g. moon or a different altitude on the earth, or for other units.

**Ballistic Max Height**, is used in 5 calculators and 1 equation/constant.

**Calculators**

**Equations and Constants **