The process of vector addition is like following a treasure map. ARRRR, Ye best learn your vectors!

N S W E Go 10 paces North

N S W E A B C D E R This is called the resultant vector. R = A+B+C+D+E X

N S W E Add the same vectors in a different order. B

N S W E The vector sum does not depend on the order of addition. R=B +A+E+D+C

Vector Addition: Using the "head to tail" graphing method Vector Addition:

A vector has components. If the components are on the axes they are called rectangular components. The sum of a vector’s components equals the vector. X component of A Y component of A A

A vector and its components are interchangeable. You can either use the vector or its components, depending on which is easier.

 A Consider this triangle… Hypotenuse Opposite Side (A y ) Adjacent Side (A x ) SOH CAH TOA

Adding Vectors in Real Life… Step 1: Draw a Vector Diagram A=10.0 m 20. o B=15 m 30. o C=10. 0 m Find The Sum of A + B + C

Adding Vectors in Real Life… Step 2: Create data table holding x and y components of each vector and the total x and y components of the resultant vector. A=10.0 m 20. o B= o C=10.0 m

A=10.0 m 20. o B=15. m 30. o C=10.0 m 10.0cos sin20 15sin30 15cos30 X X m3.420 m 7.50 m m m XY C B A

Step 3: Add the vectors along each axis to get the total resultant x and y components m3.420 m 7.50 m-13.0 m m XY C B A Total -3.6 m0.92 m Remember: When adding you round to the least amount of decimal places (but don’t round until the end!)

0.92 m 3.6 m Step 4: Draw a Vector Diagram showing only the vector axis sums from step 3. I dropped the negative sign because the arrow is pointing in the negative x direction

0.92 m 3.6 m R 2 =(3.6) 2 + (0.92) 2 R = 3.7 m Step 5: Use the Pythagorean Theorem (a 2 + b 2 = c 2 ) to find the magnitude of the resultant vector. R = 4 m

3.6 m R  Step 6a: Use a trig function (usually tan) to find the angle m 10 o

3.6 R  R = 4 10 o North of West Step 6b: Specify both magnitude and direction of the vector m

Wow! That’s so much work!

25.0 m 10.0 m 20. o 25cos20 o = sin20 o = 8.55 X Example: Add the vectors below m-8.55 m 0 m-10.0 m XY TOTAL B A 13.5 m-8.55 m

Example: Add the vectors below m 13.5 m R R 2 = =16.0 m Tan  = 8.55/13.5  = 32.3 o  16.0 m, 32.3 o south of east.