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Vector Components

Vector Components. Original Vector. Y component Vector V Y. X component Vector V X. Component – Means to be a piece, or apart, of something bigger A Component Vector is a smaller vector that is apart of a larger one. WHAT’S THE SHAPE?.

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Vector Components

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  1. Vector Components

  2. Original Vector Y component Vector VY XcomponentVector VX Component – Means to be a piece, or apart, of something bigger A Component Vector is a smaller vector that is apart of a larger one WHAT’S THE SHAPE? LOOK AT THE VECTOR,AND THE AXES. WHAT SHAPE CAN YOU MAKE?

  3. TRIGONOMETRY • SINE  = opposite/hypotenuse • COS  = adjacent/hypotenuse • TAN  = opposite/adjacent • SOH - CAH - TOA Hypotenuse Opposite  Adjacent

  4. What is a component Use Sine and Cosine: Vector (V) y component (VY) Sin  = Y/V VY = V*Sin   x component (VX) Cos  = X/V VX = V*Cos  A components is a smaller part of a larger vector. When you add up all the components (by tip tail of course) you get the original vector. These components are found by the use of the Sine and Cosine functions

  5. + and – for X components An X component vector can only point along the X axis. So it has only two possible directions (0 and 180 degrees) instead of always writing down the angle we simple use +/- signs to indicate the direction (+ for going to the right, - for going to the left) 20 m 20 m 30O 30O Vx = 17.32 m Vx = -17.32 m

  6. + and – for Y components An Y component vector can only point along the Y axis. So it has only two possible directions (90 and 270 degrees) instead of always writing down the angle we simple use +/- signs to indicate the direction (+ for going to the right, - for going to the left) 20 m VY = 5 m 30O 30O VY = -5 m 20 m

  7. Always measure from the + X axis In order for the cosine and sine functions to work properly when breaking the vectors into components, the angle that we use in the calculations must always be measured from the + X axis. 20 m 30O Vx = 17.32 m 20 m 150O 30O Vx = 20m *Cos 150 Vx = 20m *(-.866) Vx = -17.32 m

  8. Sample problem Find the X and Y components to a vector who’s length is 20m and is pointing 30 degrees below the negative X axis. 30O 20 m 210O 20 m

  9. Vx = 20m *Cos 210 Vx = 20m *(-.866) Vx = -17.32 m VY = 20m *Sin 210 VY = 20m *(-.5) VY = -10 m 20 m Both components are negative because the X is pointing to the left, and the Y is pointing down

  10. Finding the components Find the X and Y comports for the two vectors shown. 10 m

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