Ballistic Flight Horizontal Velocity

The Ballistic Flight Horizontal Velocity calculator computes the horizontal (x component) velocity of a ballistic flight based on an initial velocity and a launch angle.

INSTRUCTIONS: Choose units and enter the following:

• (V₀) Magnitude of Initial Velocity
• (Θ) Launch Angle

Horizontal Velocity (Vx):  The calculator returns the velocity in meters per second.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

At the instant of launch, before any friction has slowed the launched projectile, the object has a vertical velocity and a horizontal velocity.  This calculator computes the horizontal velocity.

The Ballistic Velocity (horizontal) equation calculates an object's velocity in the x direction, the horizontal component of its ballistic trajectory.¹  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 perpendicular to the x-component of motion, the gravitational acceleration does not affect the ballistic x-velocity.  The x-component of velocity remains constant.  The formula for the horizontal velocity is:

   v_x = V₀ • cos(θ)

where:

• v_x is the horizontal velocity
• V₀ is the initial velocity
• θ is the launch angle

Ballistic Flight Calculators:

• Ballistic Maximum Altitude:  This is the maximum altitude achieved in free ballistic flight.
• Ballistic Maximum Range:  This is the maximum horizontal range.
• Ballistic Flight Time:  This is the time duration of free flight.
• Simplified Ballistic Range: This is the range with no initial elevation above the plane.
• Ballistic Vertical Velocity: This is the vertical velocity at a given time.
• Ballistic Horizontal Velocity: This is horizontal velocity or ground speed.
• Vertical Position (Y) in Ballistic Flight: This compute the vertical position (y) at a given time within ballistic flight.
• Horizontal Position (X) in Ballistic Flight: This compute the horizontal position (x) at a given time within ballistic flight..
• 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
• Velocity to achieve a Max Ballistic Height: This computes the initial velocity required to achieve the max height.
• International Gravity Equation
• Force of Earth's Gravity
• Force of Drag

1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 81, eq 3.22