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Method #2: Resolution into Components

Method #2: Resolution into Components. Solving Vector Problems using the Component Method. Each vector is replaced by two perpendicular vectors called components. Turn every vector into a right triangle.

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Method #2: Resolution into Components

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  1. Method #2: Resolution into Components

  2. Solving Vector Problems using the Component Method • Each vector is replaced by two perpendicular vectors called components. • Turn every vector into a right triangle. • Add the x-components and the y-components to find the x- and y-components of the resultant. • Use the Pythagorean theorem and the tangent function to find the magnitude and direction of the resultant.

  3. Quick Review Right Triangle c is the hypotenuse A B c2 = a2 + b2 sin = opp/hyp cos = adj/hyp tan = opp/adj c A + B + C = 180° a transverse line crossing parallel lines: A =A A+ B = 90 ° C A A b

  4. Let’s look at one vector’s components: To resolve a vector into perpendicular components 100 37o Construct a line parallel to x through tail Construct a line parallel to y through head Arrows point the way from tail to head 100 Using trig functions solve for x & y y X = 100cos 37o = 80 Y = 100sin 37o = 60 37o x

  5. Why is this important? Components of Force y x

  6. Method #2: Adding Vectors By Resolution into ComponentsUSE COLOR PENCILS! Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat. Don’t measure anything for this method!

  7. Method #2: Adding Vectors By Resolution into ComponentsUSE COLOR PENCILS! Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat. Don’t measure anything for this method!

  8. Method #2: Adding Vectors By Resolution into ComponentsUSE COLOR PENCILS! Stan is trying to rescue Kyle from drowning. Stan gets in a boat and travels at 6 m/s at 20o N of E, but there is a current of 4 m/s in the direction of 20o E of N. Find the velocity of the boat. Don’t measure anything for this method!

  9. Solve the following problem using the component method. 10 km at 30 N of E 6 km at 30 W of N

  10. Solve the following problem using the component method. 10 km at 30 N of E 6 km at 30 W of N Rx = Ax - Bx Bx 1. Solve for components using: SOH CAH TOA 2. Solve RESULTANT using: R2 = Rx2 +Ry2 tan Ө = Rx/Ry By R Ry = Ay + By Ay Ax

  11. Another Example: 5 N at 30° N of E 6 N at 45° 6 45° 5 30° R = (0.09)2 + (6.74)2 R = 6.74 N tan  = 6.74/0.09  = 89.2°

  12. Can be used for any number of vectors. All vectors are added at one time. Only a limited number of mathematical equations must be used. Least time consuming method for multiple vectors. Advantages of the Component Method:

  13. And Another Example: y 37o 30 50 x neither parallel to x or y 37o parallel to x 30 50

  14. Continued… 37o 30 90 – 37 = 53o y x 30 y 24 24 53o = x 50 18 68 X = 30 Cos 53o = 18 Y = 30 Sin 53o = 24

  15. Neither Parallel nor Perpendicular Vector Addition (con) For these perpendicular vectors 24 68 Find resultant magnitude & direction R 24 R2 = 682 + 242 R = 72.1 θ 68 tan θ = 24/68 = tan-1 24/68 = 19.4o N of E

  16. This completes Method Two! So lets keep And practice some more! problems #3, 4 due tomorrow

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