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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.



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