# Ballistic Y Velocity

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V_y(t) =
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vCalc.Ballistic Y Velocity
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The Vertical Velocity calculator computes the vertical (y component) velocity based on an initial velocity, launch angle, and time.

INSTRUCTIONS: Choose units and enter the following:

• (V0) This is the magnitude of the initial velocity
• (Θ) This is the launch angle
• (t) This is the time into the ballistic flight.

Vertical Velocity (Vy):  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

The Ballistic Vertical Velocity equation  calculates an object's velocity in the y direction, the vertical 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 parallel to the y-component of motion, the gravitational acceleration  is the only affect the ballistic y-velocity.  The y-component of velocity changes based on the time and the constant acceleration.  The formula for the vertical velocity is:

Vy = V0 • sin(θ) - g•t

where:

# References

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 3.23