Vector Addition PhET WS https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html Graphical method: To find the resultant vector 5 = A + B + C + put the tail of vector B on the tip(head) of vector A, then the resultant vector S is the vector that starts from the tail of A to the tip(head) of B, etc. 20 10 10 :0 18 7 22 20 30 40 Using the simulation add the following vectors. Go to Explore 2D Click and drag vectors onto the graph. Adjust the magnitude and length by clicking and dragging on the tip of the arrow. Vectors do not need to start at the origin. (The origin can be moved.) Use the y-direction as north and x direction as east. Add vectors tip to tail. - Click on box next to Sum Move the sum vector so that its tail is at the tail of the first vector. The box above the graph displaces the magnitude and direction of the vector that is currently selected. Include a screenshot for each problem made when the sum vector is selected. 1. Alice drives 12 km [N] and then 15 km [E] and finally 4 km [S]. What is her total displacement? (Include magnitude and direction.) 2. Bob drives 14 km [N 20E] and then 32 km [E 25S]. What is his total displacement? (Include magnitude and direction.) 3. Chad drives 22 km [S 50W] and then 42 km [E 10N] and finally 11 km [W]. What is his total displacement? Analytical method: 1. Resolve each vector into its components. A = AN[N] + A [E] B = BN[N] + BE[E] 2. The north component of the resultant SN = AN+BN + 3. The east component of the resultant SEAE + BE + 4. The magnitude of resultant vector S = (SN) + (SE) 5. The direction of the resultant vector -1SE 0 = tan-1 (S) SN Using the simulation add the following vectors still using Explore 2D. Select the top right option for Components. Include a screenshot for each problem made with the sum vector selected. 1. Drew rode her bike 20 km [N] and then 15 km [W] and finally 5 km [S]. Complete the following table. Displacement b Magnitude Direction N component E component 2. Eileen rode her bike 7 km [N] and then 15.5 km [N75E] and finally 8.2 km [E14S]. Complete the following table. Displacement 10 10 10 TS b Magnitude Direction N component E component 3. Filip drove 98.5 km [S24W] and then 153 km [N52W] and finally 195 km [E18S]. Complete the following table. (Scale these vectors to fit on the graph given.) Scale: Displacement b TCTS Magnitude Direction N component E component