Velocity of a Projectile

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The Components of the Velocity

We know that the vertical motion of a projectile is the same as its motion would be in free fall. Therefore, the vertical component of its velocity changes by 10 m/s (actually 9.8 m/s) each second.

We also know that the horizontal motion of a projectile is at constant velocity - if it starts at 5 m/s (for instance), the horizontal component of its velocity remains 5 m/s until it hits the ground.

Finding the Velocity from its Components

If you know the horizontal and vertical velocity components, you can find the magnitude of the projectile's velocity and the projectile's direction of motion as follows:

1. Draw the horizontal and vertical velocity components (to scale) starting from a common point.
   
   
2. Draw 2 more sides to complete a rectangle.
   
   
3. The velocity of the projectile is the diagonal of the rectangle that starts at the point from which you drew the velocity components.
   
   
4. You can determine the magnitude of the velocity by measuring the scale drawing or using the Pythagorean Theorem.
   
   
5. You can determine the angle that the velocity makes with the horizontal (or vertical) by measuring the scale drawing with a protractor, or using trigonometry.

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