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Vectors

Vectors. Adding Vectors. Parallelogram Method. Head to Tail. A+B=B+A Vector Addition Commutes. Components. Components Add A + B = R. ⃗ ⃗ ⃗. Chap 3:10. Our Equations are Vector Equations. v avg = (v 1 + v 2 ) / 2

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Vectors

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  1. Vectors

  2. Adding Vectors Parallelogram Method Head to Tail A+B=B+AVector Addition Commutes

  3. Components

  4. Components AddA + B = R ⃗ ⃗ ⃗ Chap 3:10

  5. Our Equations are Vector Equations • vavg = (v1 + v2) / 2 • To multiply or divide a vector by a number • Multiply or divide the magnitude • Leave the direction the same

  6. Acceleration • An arrow is shot with an intial speed of 60 m/sec at an angle of 60° with the horizontal. After 4 seconds how fast is it going? • v2 = v1 + gt • Scale 10m/sec = 1cm • t = 4 s • g = 10m/s2 down • gt = 10m/s2 ∙ 4s = 40m/sdown

  7. Components • v2 = v1 + at • v1 = 60 m/sec 60° N of E • Horizontal = v1x = v1 ∙ cos 60° = 30 m/s • Vertical = v1y = v1 ∙ sin 60° = 52 m/s • a= g = 10 m/s2 down • Horizontal = ax =0 Vertical = ay = −10 m/s2 • at = 10m/s2 ∙ 4s • Horizontal = axt=0 Vertical = ayt= −40 m/s

  8. To Add, Add Components horizvert v1 v1x = v1∙cos60° v1y=v1∙sin 60° 30 m/s 52 m/s at axt=0 ayt= −40 m/s v2=v1+at 30 m/s 12m/s Magnitude = v2 = √(302 +122) = √1044 = 32.3m/s Direction of v2 tan θ =v2y/v2x = 12/30= .4 θ=tan-1 .4 = 21.8°

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