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# Projectile Motion - Vertical Displacement

vCalc.Projectile Motion - Vertical Displacement

The **Vertical Displacement for a Projectile** calculator computes the vertical distance from an origin of an object after time (**t**) based on its initial position from the origin (`Y_0`), it's initial velocity (`V_y0`) and a constant acceleration due to gravity (**g**).

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

- (
**y**) This is the initial displacement in the y direction at time zero (t_{0}_{0}). - (
**v**) This is the initial y-component velocity at time zero (t_{y0}_{0}). - (
**t**) This is the time into ballistic flight, some time after time zero (t_{0}).

**Vertical Displacement (y):** The calculator will return the vertical displacement in meters. However, this can be automatically converted to other length units via the pull-down menu.

### Ballistic Flight Calculators

- Ballistic Max Range: This is the maximum horizontal range.
- Ballistic Max Height: This is the maximum altitude in free ballistic flight.
- Ballistic Travel Time: This is the time duration of free flight.
- Velocity to Achieve Max Height: This computes the initial velocity at a launch angle needed to reach a max height.
- Initial Horizontal Velocity: This is horizontal velocity or ground speed.
- Initial Vertical Velocity: This is the vertical velocity at a given time.
- Ballistic Position at Time (t): This compute the position (x,y) at a given time within ballistic flight, where x is distance down range and y is the height above the plane.
- Ballistic Parabolic Equation provides the parabolic flight position equation based on the launch speed, height and angle.
- Acceleration Due to Gravity at Sea Level

### General Information

This is the typical equation for an object launched vertically against gravity or a projectile in a ballistic trajectory. The formula for the vertical displacement is:

y = y_{0} + v_{y0}•t - 0.5•g•t^{2}

where:

- y is the vertical displacement
- y
_{0}is the initial vertical displacement. - v
_{y}0 is the initial vertical velocity - g is the acceleration due to gravity
- t is duration of time.

This equation allows the input value for **g** to be an input, so the acceleration constant for other bodies, like the Moon could be input and the displacement calculated for projectile motion on the Moon. The default for **g** is the Earth's gravitational acceleration near sea level.

**Projectile Motion - Vertical Displacement**, is used in 2 calculators.

**Calculators**