Vectors
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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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Vectors

Vectors


Adding vectors

Adding Vectors

Parallelogram Method

Head to Tail

A+B=B+AVector Addition Commutes


Components

Components


Components add a b r

Components AddA + B = R

⃗ ⃗ ⃗

Chap 3:10


Our equations are vector equations

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


Acceleration

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


Components1

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


To add add components

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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