## Projectile Motion

#### (Illustration)

Please wait for the animation to completely load.

A purple projectile is projected as shown in the animation (position is given in meters and time is given in seconds).  The blue and red objects illustrate the x motion and y motion of the projectile.  Restart.

Any multidimensional motion can be resolved into its components.  Thus, to understand projectile motion, you must understand the x-motion and y-motion separately.

Consider the x-direction.  Notice that the x-coordinate of the projectile (purple) is identical to the x-coordinate of the blue object at every instant.  What do you notice about the spacing between blue images?  You should notice that the displacement between successive images is constant.  So what does this tell you about the x-velocity of the projectile?  What does it tell you about the x-acceleration of the projectile?

Consider the y-direction. Notice that the y-coordinate of the projectile (purple) is identical to the y-coordinate of the red object at every instant.  What do you notice about the spacing between successive images for the red object?  You should notice that the displacement between successive images gets smaller as the object rises and gets larger as the object falls.  This means that it has a downward acceleration.  By studying the graphs, we can also see that the y-acceleration is constant.

A particularly important point to understand for the motion of a projectile is the peak.  What is the velocity of the projectile at the peak?  This is a tricky question because you have a good idea that the y-velocity is zero.  However, does this mean that the velocity is zero?  Remember that velocity has two components, vx and vy. At the peak, vx is not zero.  Therefore, the velocity at the peak is not zero.  Click here to view the velocity and acceleration vectors.

Illustration authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.