1. The Analytical Method of Finding the Resultant Used to find the resultant when: 1)only two vectors are present. 2) two vectors are perpendicular.

2. Given two vectors: A B A=A, NorthB=B, West A B R A B

3. R B A θ θ= tan -1 (B/A) R = R, θ W of N R=A+B A B Ф = tan -1 (A/B) θ R= R, Ф N of W R=B+A R Ф

4. Example 1: A B A B R A=9.0 N, 90° B=12 N, 180 θ=tan -1 (12N/9N)=53° B θ=53° W of N Ф=tan -1 (9 N/12N)=37° Ф θ = 37° N of W What is the resultant force as a force of 9.0 N acts to the north while a 12 N force acts to the west? θ A A B R

5. R=15N, 53º W of N R=15N, 37º N of W or

6. Example 2 What is the resulting displacement of a plane that travels 100 km south and then 65 km to the west? 1.2x10 2 km, 33° W of S or 1.2x10 2 km, 57°S of W