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P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors

P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors. Objectives: We differentiate a scalar and vector We will add and resolve vectors. Scalar vs. Vector. Scalar  only magnitude (numerical value) Vector  magnitude and direction. Distance Speed

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P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors

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

  2. 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

  3. 75.2 degrees 55 km west 33.0 m/s @ 19.0o 98.4 m 8 m to the left 14.0 cm 16 km NW 25 km/h Scalar or Vector Scalar Vector Vector Scalar Vector Vector Scalar Scalar

  4. Vectors • Represented with an arrow Length = Magnitude θ Angle = Direction

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

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

  7. Adding Vectors • Resultant: Sum of two or more vectors Magnitude  Direction  hypotenuse opposite θ adjacent

  8. 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 x θ xo

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

  10. Which hits the ground first? g g

  11. Demo

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

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

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

  15. Determining Hang Time of aHorizontally Launched Projectile • If projectile is horizontally launched then vi(y) = 0 • Determine yiand yf yo   y

  16. Determining the Range of a Horizontally Launched Projectile • If projectile is horizontally launched all velocity viis in x-dir vi= vi(x) • Determine time using y direction vo = vo(x)

  17. 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 vo = 2.98 m/s

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