1. Vectors

2. OK, so what are these vector thingamajigs? A vector is a value / measurement A vector is a value / measurement Vectors have MAGNITUDE and DIRECTION Vectors have MAGNITUDE and DIRECTION –Displacement, velocity, acceleration, force, momentum, etc. –As opposed to a SCALAR which only has magnitude (mass, temperature, time, etc.) Use an ARROWto represent the value Use an ARROWto represent the value

3. Remember… Don’t make this harder than it needs to be Don’t make this harder than it needs to be We use arrows to represent ANY vector to SIMPLIFY things We use arrows to represent ANY vector to SIMPLIFY things We can then use GEOMETRY / TRIG to break the vectors down We can then use GEOMETRY / TRIG to break the vectors down

4. EXAMPLES A car moves to the right 286 m x y 286 m DISPLACEMENT VECTOR

5. EXAMPLES A girl walks south at 0.2 m/s E N 0.2 m/s VELOCITY VECTOR

6. EXAMPLES A person pulling a rope to the left 30° above the horizontal with a force of 10 N x y 10 N FORCE VECTOR 30°

7. Adding Vectors A + B = B + A = R (Resultant) A + B = B + A = R (Resultant) ALWAYS add Tip To Tail (T 3 ) ALWAYS add Tip To Tail (T 3 ) x y A B R B A A B

8. EXAMPLE: You are crossing a river: You are crossing a river: –Current is moving at 1.2 m/s –You can swim at 0.85 m/s NO CURRENT vsvs + v c = v R

9. Vector Components Every vector has an x and y component (depends on coordinates) Every vector has an x and y component (depends on coordinates) x y A AxAx AyAy AxAx + A y = A

10. Solving for Components x y 30° A = 15 m/s AxAx AyAy

11. Components x y θ V 0x V 0y V0V0

12. Practice Problem #1 You are lost in the wilderness and when you try to go and find help, you just end up getting more lost. You realize you walked (from your starting point) 264 m at 280° and 118 m at 25° (all compass headings). What is your final displacement from your start? You are lost in the wilderness and when you try to go and find help, you just end up getting more lost. You realize you walked (from your starting point) 264 m at 280° and 118 m at 25° (all compass headings). What is your final displacement from your start?