# Classical Mechanics and Projectile Moves Assignment

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When an object (stone, spear, arrow or bullet) is thrown, hurled or shot in the air, the object is a PROJECTILE (“Projectile”). The study of projectile is important because it must be realized that they are very much part of man’s daily life then and now. Whether man likes it or not, he encounters and uses projectile in his everyday life. Our hunting ancestors threw stones and spears on animals to kill them for their food.

In today’s sports, balls follow projectile motion such as when a basketball player shoots the ball into the hoop, a golfer or a baseball player hitting the ball, a tennis player lobbing the ball, a javelin thrower, a discus thrower or a shot putter trying to throw their objects as far as they can (Sears, Zemansky and Young 54). In warfare, catapults and arrows in medieval times were the deadly weapons while today, guns, mortars, rockets and missiles have replaced those ancient weapons of war (“Field Artillery and Mortars”, “Ballistics”). However, the way to effectively use these weapons has not changed.

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They are to be launched into projectile motion to hit the target. The path followed by a projectile is called its trajectory. Projectiles follow a curved trajectory or curved path that is a PARABOLA. (Sears, Zemansky and Young 54, Briggs 491). It is actually easy to observe projectile motion when we use a light material as the projectile. For example, crumple a sheet of bond paper into a small ball. On a standing position, throw the paper ball straight horizontally. Observe that as the ball moves, it curves downward. Even if you try to throw it harder, it will still follow a curved downward path but will land farther.

So, the harder you throw the object straight horizontally, the farther it will land. The distance where the object lands measured horizontally from the point you threw it to the point where it landed is called the RANGE of the projectile. The range of the projectile can be increased by throwing it at an angle instead of straight horizontally. It was Galileo Galilei who first accurately described projectile motion. He showed that projectile motion is an object moving in two dimensions. It has a vertical and horizontal component. Projectiles could be best understood when we separately analyze its components of motion.

This type of analysis was at that time revolutionary and innovative in nature because no one did such analysis in the same manner as Galileo. He showed that the vertical component of the projectile motion was that of a freely falling body and therefore the projectile moves with acceleration due to gravity g = 9. 8 m/s2. Its horizontal component was of a constant velocity motion (Jones and Childers 81). Let us imagine right now that there is no gravity. If we throw something in the air horizontally, the object will “float” and move in a straight line with constant velocity. The magnitude of the velocity is the velocity at the point of release.

A constant velocity motion without gravity is illustrated below. o o o o o Time:t= 0 sec t=1sec t=2 sec t=3 sec t=5 sec Figure 3: Constant velocity motion means the same magnitude of velocity all through its motion If an object is dropped from a certain height will move downward in an accelerated motion because of an existing gravity. When we say accelerated motion, its velocity constantly increases or falls down faster and faster each time and the distance it travels becomes greater each time (Hewitt 178, Sears, Zemansky and Young 37).

The motion of a free falling body due to gravity is shown below. time = 0 sec o time = 1 sec o time = 2 sec o time = 3 sec o Figure 4: Accelerated Motion (Free Fall): The downward velocity of the object increases each time as shown by the arrow scaled according to the magnitude of the velocity. The distance traveled each second is also noticeably increasing each time. Now, let gravity exist and we throw the object again horizontally. The object will be expected to move with constant velocity as before but gravity will make the object accelerate or move downward.

The combination of these constant horizontal motion and accelerated vertical motion is that of projectile motion. Hence, we scientifically define projectile as any body given an initial velocity and then follows a path determined by the effects of gravity and air friction. The curved path or trajectory of a projectile is a parabola (Hewitt 179). REFERENCES “Ballistics. ” World Book. CD-ROM. Chicago: World Book, Inc. 2005. Briggs, Michael M. “Ballistic Missile”. McGraw-Hill Encyclopedia of Science and Technology. 8th ed. USA: McGraw-Hill Inc. , 1997. Vol. 2: 491-492. “Field Artillery and Mortars”. Rockets/Missiles. 2006.

FindArticles. com. 30 Sept. 2006. <http://www. findarticles. com/p/articles/mi_qa3723/is_200410/ ai_n9446468>. Hewitt, Paul G. Conceptual Physics. 9th ed. USA: Pearson Educational Publishing. 2002. Jones, Edwin R. , and Richard L. Childers. Contemporary College Physics. 3rd ed. USA: WCB/McGraw-Hill Companies, Inc. , 1999. “Projectile. ” Microsoft Encarta. CD-ROM. Redmond, WA, USA: Microsoft Corporation 2005. Sears, Francis W. , et. al. College Physics. 7th ed. USA: Addison-Wesley Publishing Company Inc. , 1991. Tipler, Paul A. Physics for Scientists and Engineers. 4th ed. New York: W. H. Freeman and Company, 1999.

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