# Ballistic Position (X,Y)

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The Ballistic Position calculator computes the vertical (y component) and horizontal (x) position based on an initial velocity, launch angle, and time.

INSTRUCTIONS: Choose units and enter the following:

• (V) This is the magnitude of the initial velocity
• (Θ) This is the launch angle
• (t) This is the time into the ballistic flight.
• (h) This is the initial height above the plane.

Position (x,y):  The calculator returns the relative position in meters, where x is the distance down range and y is height above the plane.

#### The Math / Science

This calculator first computes the maximum flight time.  If the time entered is greater than the max flight time, the time is set to the max flight time in order to compute the X, Y position.  This implies that the object is at rest after the max flight time.

The Ballistic Vertical Position equation  calculates an object's position in the y direction, the vertical component of its ballistic trajectory.  This is the equation for the ideal projectile, which means it neglects external forces such as air resistance. Since in the ideal projectile motion model the force of gravity is the only force component affecting the trajectory, and the force of gravity is parallel to the y-component of motion, the gravitational acceleration  is the only affect the ballistic y-velocity.  The y-component of position changes based on the time and the constant acceleration.  The formula for the vertical position is:

y = h + sin(Θ)•V•t - ½gt²

where:

The Ballistic Horizontal Position equation  calculates an object's position in the x direction, the horizontal component of its ballistic trajectory.  This is the equation for the ideal projectile, which means it neglects external forces such as air resistance. Since in the ideal projectile motion model the force of gravity is the only force component affecting the trajectory, and the force of gravity is parallel to the y-component of motion, the gravitational acceleration  has no affect the ballistic x-velocity.  The x-component of position changes based on the time and the horizontal velocity.  The formula for the horizontal position is:

x = cos(Θ)•V•t

where:

• x is the horizontal position
• V0 is the initial velocity
• θ is the launch angle
• t is the time into the flight