Labs - Projectile Motion Introduction There are very few...

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Projectile Motion Introduction There are very few situations in which an object is projected straight up into the air. Think of the way balls travel when shot in various sports, think of water in a fountain or pond is sometimes shot straight up. In most of these cases, objects that are thrown, shot, flung, exploded, or driven upward, the objects have some initial horizontal component of velocity which will cause them to land at a position that is different from their takeoff point. How far away the object lands or how high it goes in the air is information that might be vitally important to know. For instance, if one is trying to jump a car across a broken section of bridge (a normal scenario for any action film), it is good to know what velocity one must achieve before leaving the ground so as to land at the appropriate site on the other side of the chasm. Someone who is shooting fireworks needs to be sure that the rocket achieves a given height before it explodes. Sometimes, you will need to know both how high and how far an object will go, as when a person shoots a basketball over the outstretched hands of a defender while trying to put the ball in the basket. For this kind of information, we need to develop a model for how an object will move in two dimensions. Theory After being propelled into the air, a freely moving object is only subject to two forces: gravity and air resistance. The force of gravity will be a constant and pointing only in the vertical direction, whereas the air resistance will depend upon the velocity of the object and will point in the opposite direction of the velocity. The faster it moves, the greater the force of air resistance. Furthermore, as the velocity of the object changes direction, so will the air resistance. To include air resistance in our model would complicate it beyond our ability to solve for the object’s motion in this class. Fig. 1: July 4 th Fireworks ( NPS ) Luckily, its effect is usually quite small for objects that are not moving too fast, whose mass is not too small, and whose surface area is not too large. For instance, we can ignore air resistance when we throw a basketball or a hammer. The effect of air resistance in these cases is small enough that its effect on the outcome is negligible. In studying the motion of such objects it is easier mathematically to decouple motion in the horizontal direction from motion in the vertical direction. The only thing that ties them together is time. In this case, we know that we have no acceleration in the horizontal (x-direction) and
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Labs - Projectile Motion Introduction There are very few...

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