1. Component Vectors Vectors have two parts (components) –X component – along the x axis –Y component – along the y axis

2. Finding components X component – follow from the tail of the vector along the x axis until you reach the point where the tip would be if it fell straight down

3. Y component – follow from where you stopped on the x axis straight up to the tip You should now have formed a right triangle with the original vector as the hypotenuse

8. To find components To find components, you must use trigonometric functions Hypotenuse Adjacent Opposite ø

9. Trig functions Θ is the angle between the vector and the x axis sin Θ = _opposite_ hypotenuse cos Θ = _adjacent_ hypotenuse tan Θ = _opposite_ adjacent

10. Steps for finding the components 1)Draw a picture (arrowheads, original vector & components) 2)Choose a trig function 3)Use algebra to solve for the desired variable & plug in 4)Calculator in degrees! 5)Check with Pythagorean theorem

11. Example

12. X component cos Θ = _adjacent_ hypotenuse cos 35 = _adjacent_ 316 316 cos 35 = adjacent 259 N = adjacent

13. Y component sin Θ = _opposite_ hypotenuse sin 35 = _opposite_ 316 316 sin 35 = opposite 181 N = opposite

14. How to find components when you add two vectors 1)Find the x and y component for both vectors 2)Add up the x components 3)Add up the y components 4)Draw a new set of vectors 5)Use Pythagorean theorem to get the magnitude of the resultant vector 6)Use arctangent to get the angle of the new vector

16. Vector d 1 X component adj = hyp cos Θ adj = 36 cos34º adj = + 29.8 m Y component opp = hyp sin Θ opp = 36 sin34º opp = +20.1 m

17. X component opp = hyp sin Ø opp = 23 sin64º opp = - 20.7 m Y component adj = hyp cos Θ adj = 23 cos64º adj = +10.1 m Vector d 2

18. Total X displacement – add d 1 and d 2 d total = d 1 + d 2 d total = 29.8 m + (-20.7m) d total = +9.1m

19. Total Y displacement – add d 1 and d 2 d total = d 1 + d 2 d total = 20.1 m + 10.1m d total = +30.2m

20. To get the magnitude of the resultant vector Use Pythagorean Theorem d Total = ( d X ) 2 + ( d y ) 2 d Total = ( 9.1) 2 + ( 30.2) 2 d Total = 82.81 + 912.04 d Total = 994.85=31.5 m

21. To find the angle of the resultant vector Use arctangent function: Θ = tan -1 (opp/adj) Θ = tan -1 (30.2/9.1) Θ = tan -1 (3.3) Θ = 73.1°

22. Formulas a 2 + b 2 = c 2 R 2 = a 2 + b 2 - 2ab(cos θ) SOH CAH TOA