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UT PHY 317K - Motion in Two and Three Dimensions
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PHY 317K 1st Edition Lecture 3 Outline of Last LectureI. Average MotionII. Instantaneous VelocityIII. AccelerationIV. The Five Big EquationsOutline of Current LectureI. VectorsII. Projectile MotionCurrent LectureVectors:- Vectors express both a magnitude and a direction- Scalars are only quantities, they have no direction- Vectors can only be added “tip to tail”o To add two vectors, put the secondvector’s tail at the head of the firsto The sum is then the vector that extendsfrom the tail of the first vector to the headof the second (This is the resultant vector)- The magnitude and direction of a resultant vectorcan be found by:Projectile Motion:- Treat the x and y components of the projectile motion separately- The y (vertical) direction determines how long the object is in the air (time)- When there is a constant gravitational acceleration:o Vx = vx0  The horizontal final velocity is equal to the initial horizontal velocityo Vy = Vy0 – gt  The final vertical velocity is equal to the initial vertical velocity minus gravity multiplied by timeo X = X0 + Vx0t  The horizontal distance is equal to the initial horizontal position plus the initial horizontal velocity multiplied by timeo Y = Y0 + Vy0t – ½ gt^2  The final vertical position is equal to the initial vertical position plus the initial vertical velocity multiplied by time subtracted by ½ of gravity time squared- The maximum range can be achieved with a 45 degree


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