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P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors Objectives: 1)We differentiate a scalar and vector 2)We will add and resolve vectors

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Scalar vs. Vector Scalar only magnitude (numerical value) Vector magnitude and direction Distance Speed Mass Temperature Volume Energy Density Power Work Displacement Velocity Acceleration Force Momentum Weight

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Scalar or Vector 1)75.2 degrees 2)55 km west 3)33.0 m/s @ 19.0 o 4)98.4 m 5)8 m to the left 6)14.0 cm 7)16 km NW 8)25 km/h Scalar Vector Scalar Vector Scalar Vector Scalar

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Vectors Represented with an arrow Length = Magnitude Angle = Directionθ

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Adding Vectors Rules: added in any order moved maintaining orientation added tip-to-tail 3 m east 4 m north Resultant = 5 m NE

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Adding Vectors Which of the following is the correct orientation for adding these two vectors? WRONG RIGHT

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Adding Vectors adjacent opposite hypotenuse θ

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In-Class Example #1 Tom leaves home and drives 3 km north and then 5 km east to get to work. What is the total distance travelled and his total displacement? ∆x = 5.83 km θ xoxo x

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Projectile Projectile: An object thrown/launched and curves due to gravity Path: Trajectory Shape: Parabola

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Which hits the ground first? gg

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Demo

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Which hits the ground first? Motion in the x and y directions are independent of each other

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Projectile Motion x-dir motion not affected by gravity (y-dir)

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Projectile Motion Gravity (y-dir) not affected by x-dir motion

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Determining Hang Time of a Horizontally Launched Projectile If projectile is horizontally launched then v i(y) = 0 Determine y i and y f yo yo y

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Determining the Range of a Horizontally Launched Projectile If projectile is horizontally launched all velocity v i is in x-dir v i = v i(x) Determine time using y direction v o = v o(x)

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In-Class Problem #1 A marble rolls off a table that is 0.85 m high and lands 1.25 m from the base of the table. a) How long was the marble in the air? b) What was the marble’s initial velocity? t = 0.42 s v o = 2.98 m/s

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Motion in Two Dimensions

Motion in Two Dimensions

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