Vectors- Motion in Two Dimensions Magnitudethe amount or size of something Scalara measurement that involves magnitude only, not direction EX: mass, time,

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Presentation transcript:

Vectors- Motion in Two Dimensions Magnitudethe amount or size of something Scalara measurement that involves magnitude only, not direction EX: mass, time, temperature, distance, speed (can never be negative) Vectorhas both magnitude and direction EX: displacement, velocity, acceleration (can be negative due to direction)

Vectors can be added and subtracted. If two vectors point in the same direction, they will add together to form a larger vector. (Largest sum) If two vectors point in opposite directions, they subtract, with the bigger vector indicating the direction of the result. (Smallest sum) EX: Vectors 6m and 5m. Same direction, sum is 11m. Opposite directions, 1m.

Resultant the final vector that represents the combination of a series of vectors. Ex: If vectors are at right angles, Use Pythagorean Thm to find Resultant. Components the x and y vectors that add together to form the resultant. EX: Vector length 10, at 30 0, find the x and y components. (draw a right triangle)

Trig functions- sine, cosine, tangent are useful to resolve the vectors into components, and to solve for missing angle. (Use only with right triangles) SOH- CAH- TOA Sinethe ratio of the side opposite the angle, and the hypotenuse. (Sine  = Opposite/Hypotenuse) Cosinethe ratio of the side adjacent the angle, and the hypotenuse. (Cosine  = Adjacent/ Hypotenuse)

Tangent the ratio of the side opposite the angle to the side adjacent to the angle. (Useful in finding missing angle measures) (Tangent  = Opposite / Adjacent) Example 1: Find the x and y components of a velocity that is 25 m/s at 40 0 to the horizontal) Example 2: A hill is 80m long, and 15m high. What is the angle of the slope?