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Vectors

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Vectors

Parallelogram Method

Head to Tail

A+B=B+AVector Addition Commutes

⃗ ⃗ ⃗

Chap 3:10

- vavg = (v1 + v2) / 2
- To multiply or divide a vector by a number
- Multiply or divide the magnitude
- Leave the direction the same

- 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

- 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

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°