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PHYSICS Vectors and Scalars

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**Useful Vector Math SOHCAHTOA sine: sin q = opp/hyp**

Trigonometry sine: sin q = opp/hyp cosine: cos q = adj/hyp tangent: tan q = opp/adj

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Useful Vector Math Pythagorean Theorum

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Vectors vs. Scalars scalars: only magnitude (size) ex. distance, time, speed, mass, temperature vectors: magnitude and a direction Examples of vectors displacement, s or x : distance and direction velocity, v : speed and direction acceleration, a: change in speed and direction

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Vector Basics Vectors displacement vectors d = d (displacement), q (direction) length proportional to amount direction measured by angle

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**Co-linear Vectors Combining Vectors resultant: vnet= v1+ v2**

Collinear vectors: v v v v2 resultant: vnet= v1+ v2 ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity? ex: A plane flies 40 m/s W with a 10 m/s W tailwind. What is the net velocity?

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**Non Co-linear Vectors Perpendicular vectors: resultant’s magnitude:**

resultant’s direction:

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**Graphical Method Tail to tip method**

+y Tail to tip method Place first vector on graph with tail starting at the origin Place the second vector with the tail at the tip of the first vector Repeat step two for multiple vectors Draw a line from the tail of the first vector to the tip of the final vector. This final vector is called the resultant. The order that you add vectors doesn’t matter (commutative property) +x -x -y

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Component Method

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Forces in 2D Chapter 5. 5.1 Vectors Both magnitude (size) and direction Magnitude always positive Can’t have a negative speed But can have a negative.

Forces in 2D Chapter 5. 5.1 Vectors Both magnitude (size) and direction Magnitude always positive Can’t have a negative speed But can have a negative.

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