Vectors

Vector and Scalar quantities Scalar quantities have size or magnitude, but a direction is not specified. (temperature, mass, speed, etc.) Vector quantities have magnitude and a specific direction (velocity, acceleration, etc.)

pg80 Physics Serway /Faugh (Holt)

Arrows Represent Vectors Vector quantities are represented by drawing arrows. The arrows are drawn to represent magnitude (size of arrow) and direction (position of arrow).

The Resultant Vector The resultant is a vector that represents the sum of two or more vectors.

Finding the Resultant Align the vector arrow tip to tail. Resultant

One way to find a resultant could be to draw the situation to scale on paper (such as 50 m = 1 cm). Measuring the length of the vector pointing from the tail of the first vector to the head the second vector, and then, multiplying by the scale. For example if line (c) is 3.0 cm the distance would be 150 meters. This is the displacement. pg81 Physics Serway /Faugh (Holt)

An example of the head-to-tail method of vector addition

Using Pythagorean theorem to find a resultants magnitude. A toy car is moving directly across a moving walkway. As the car moves in the y direction, the walkway moves in the x direction.

We can look at the diagram as a triangle. Therefore we can solve this by using the Pythagorean theorem. b c a

Use the tangent function to find the direction of the resultant. pg86 Physics Serway /Faugh (Holt)

Pythagorean and Trigonometric Equations soh cah toa

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Other helpful right triangle functions besides tangent pg88 Physics Serway /Faugh (Holt)