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Chapter 3 Projectile Motion Alta High Conceptual Physics Vectors and Scalars Vector vs. Scalars Vectors have both magnitude and direction Displacement, Velocity, Acceleration, Force, and Momentum Scalars have only magnitude Mass, Time, and Temperature Alta High Conceptual Physics Vector Addition Two Methods Graphical Method Requires a ruler and a protractor Process Convert each vector into a line that fits a scale of your choosing Draw Vectors head to tail, measuring the angle exactly Draw a resultant Measure the resultant and the resulting angle Convert the measurement back into a vector answer Alta High Conceptual Physics Graphical Addition A man drives 125 km west and then turns 45º North of West and travels an additional 100 km. What is his displacement? Step one: Set Scale 1 cm = 25 Km 100 km = 4 cm 45° Alta High 5 cm 125 km = Conceptual Physics Graphical Addition Step Two: Move Vectors Head to Tail Step Three: Draw Resultant from Tail of First Vector to the head of the last. 100 km = 4 cm 45° 125 km = 5 cm Alta High Conceptual Physics Graphical Addition Step Four: Measure the Measure the Resultant and the resulting angle. Step Five: Using the Scale, convert the 100 km = 4 cm measurement into an answer. 8.3 cm 8.3 cm * 25 Km/cm = 208 Km 45° 125 km = 5 cm 26.2° Final Answer: His displacement is 208 of West Km @ 19.9° North High Conceptual Physics Alta Components of Vectors Often we need to change a single vector into two vectors in order to make addition easier. These two vectors will be a right angles to each other and are called component vectors or just components for short. The breaking down of a vector this way is called resolution. Alta High Conceptual Physics Vector Resolution Step One: Draw Original Vector 45º 100 Km 45° North of West Alta High Conceptual Physics Vector Resolution Step Two: Draw parallelogram to Resolve Vector into components 100 Km 45° North of West Alta High Conceptual Physics Vector Resolution Step Three: Label and measure components North component = 70.7 km 45° West component = 70.7 km 100 Km 45° North of West Alta High Conceptual Physics Mathematical Addition Mathematical Addition of Vectors Requires a basic knowledge of Geometry – You must know: Sin θ = Opposite/Hypotenuse Cos θ = Adjacent/Hypotenuse Tan θ = Sin θ/ Cos θ =Opposite/Adjacent ArcSin, ArcCos, ArcTan Alta High Conceptual Physics Mathematical Addition Mathematical addition requires that you be able to Draw a rough sketch of the original vectors Draw a parallelogram Draw the Resultant Use Triangle geometry to find the magnitude and direction of the resultant Alta High Conceptual Physics Example What is the result of adding two vectors if the first vector is 100 km to the west and the second vector is 50 km to the north? Alta High Conceptual Physics Mathematical Addition Step One: Sketch the vectors Step Two: Put vectors on the same axis and draw the parallelogram 100 Km West + 50 Km North Step One Step Two Alta High Conceptual Physics Mathematical Addition Step Three: Draw the Resultant Step 4: Use Right triangle geometry to find the length of the resultant Step Four: 50 Km Since this is a right triangle you can find the resultant using Pythagorean 100 Km theorem Pythagorean Theorem: C2 = A2 + B2 111.8 Km C = SQRT(A2 + B2) = SQRT{(100)2+(50)2} =111.8 Km Step Three Alta High Conceptual Physics Graphical vs. Mathematical Methods Graphical Method Less Complicated Math Good Approximation Not as exact as you would like Mathematical Method No need for ruler or protractor Less time dedicated to sketch More Accurate result Mathematics is more difficult Alta High Conceptual Physics Projectile Motion A projectile is any object thrown or launched Uses the same kinematic equations you have already learned Requires that you use two sets of equations; one in the horizontal and one in the vertical These two sets are related only by time Alta High Conceptual Physics Projectile Motion A projectile which is dropped or thrown horizontally has an initial velocity in the Y direction (V0y) = 0 Acceleration in the horizontal direction (ax) = 0; hence Velocity in the horizontal direction (Vx) is constant This means that only one kinematic equation applies in the horizontal direction: Xx = Vxt Alta High Conceptual Physics Projectile Motion While it is moving forward, it is also falling just as if you had dropped it. So in the Y direction: x = ½ at2 Where a is the acceleration due to gravity. The one thing that both motions have in common is time. When the projectile hits the ground it stops moving in both directions! Alta High Conceptual Physics Projectile Motion A ball is thrown horizontally off a building which is 200 m high with a velocity of 10 m/s (a) How long does it take to reach the ground? (b) How far from the building will it land? (c) What is its velocity just before it hits the ground (remember magnitude and direction) Alta High Conceptual Physics Fast Moving Projectiles: Satellites A satellite is a fast moving projectile Since the projectile moves in a curved path, and the earth is a curved surface, if the projectile moved fast enough its motion would follow the curve of the earth Such a projectile would fall around the earth rather than to the earth Such a projectile becomes a satellite and orbits the earth. Alta High Conceptual Physics Problem Types Adding Vectors Resolving vectors into components Projectile Motion Alta High Conceptual Physics

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posted: | 6/2/2011 |

language: | English |

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