### Properties
of Projectile Motion

Objects experiencing projectile motion have a constant velocity in the horizontal
direction, and a constantly changing velocity in the vertical direction. The
trajectory resulting from this combination always has the shape of a parabola.
The animation at Glenbrook South High's website
illustrates this property. Go to the website and examine the motion of the three
balls. The green ball illustrates constant velocity
in the *x*-direction; the red ball illustrates
constant acceleration from gravity in the negative *y*-direction. The blue
ball illustrates projectile motion; its *x*-coordinate at any time is the
same as the *x*-coordinate of the green ball,
and its *y*-coordinate at any time is the same as the *y*-coordinate
of the red ball. Notice that the trajectory is a parabola.

As mentioned above, the time required for an object to complete its motion
is the same whether you consider the *y*-direction or the *x*-direction.
This has an interesting implication for projectile motion, particularly if the
initial vertical velocity is zero. * The time required
for initially horizontal projectile motion to occur is the same as the time
required for the object to fall to its final height. * Thus, a ball
thrown horizontally will reach the ground at the same time as a ball dropped
from the same height. This concept is illustrated by the infamous "Monkey" exercise,
contained below.

One can extend this argument and say that * the
horizontal distance traveled in projectile motion is the same as the distance
traveled by an object with just the horizontal velocity. * Another
animation by Glenbrook South High illustrates this concept with a ball thrown
upward from a moving truck. The ball has the same horizontal velocity as the
truck since it is initially moving with the truck. The ball is then given additional
vertical velocity, but its horizontal position stays the same as that of the
truck. Watch the animation at
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/vectors/tb.html and take
note of where the ball ends up.

When looking at these animations, you should remember that air resistance is being
ignored. If you were to throw a ball up in the air from the back of a truck on
your way to a friend's house (not recommended), you would find it did not land
back in your hands, but creamed the car following you (repeat, this is NOT a recommended
activity). Air resistance and wind provide additional sources of acceleration,
making the physical problem somewhat more complex than the simple projectile motion
we are considering here.

* Copyright © 1999 Rensselaer Polytechnic Institute and DJ Wagner. All Rights Reserved.*