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AIM – How do we add vectors? DO NOW – Where have you heard the word vector aside from Physics class? HW - Textbook p. 26 #67(a-d), 68(a-d), 72(a-d) V ECTOR A DDITION V ECTORS Quantities with magnitude (amount, size) and direction. Example: 20 m North or 20 m West Vectors Scalars (no direction) Displacement Velocity Acceleration Distance Speed Time Mass D RAWING V ECTORS Vectors can be drawn to graphically represent magnitude as well as direction. Length indicates magnitude, and therefore must be drawn to scale using a ruler and protractor. length The angle indicates direction, represented by θ (theta). θ Horizontal Axis = +X direction NEVER FORGET TO DRAW THE ARROWS!! R ESULTANT – A DDING V ECTORS Resultant – the result of 2 or more displacements (vectors) 20 m West R = resultant displacement θ = direction R θ 20 m North R = 28 m, 45° determined by measuring with a ruler and protractor M ATHEMATICAL T ECHNIQUES When vectors are at right angles, we can use the Pythagorean Theorem and SOHCAHTOA: a2 + b2 = c2 20 m West R2 = (20m)2 + (20m)2 √ R θ 20 m North R = 800 m2 R = 28.2 m tan θ = opp/adj = 20/20 = 1 θ = tan-1 (1) = 45° V ECTOR A DDITION ( CONT.) Same Direction: simply add = 11 m 4m 7m Opposite Direction: subtract 5m 9m =4m Practice A plane flies 1500 miles East and 200 miles South. What is the magnitude and direction of the plane’s final displacement? A hiker walks 80 m North, 20 m East, 50 m South, and 30 m West. What is the magnitude and direction of the hiker’s displacement? P RACTICE P ROBLEM #1 A plane flies 1500 miles East and 200 miles South. What is the magnitude and direction of the plane’s final displacement? **not drawn to scale** 1500 miles θ 200 miles a2 + b2 = c2 (1500 m)2 + (200 m)2 = R2 R = √ (1500 m)2 + (200 m)2 R = 1513.275 m tan θ = opp/adj θ = tan-1 (200/1500) θ = 7.5946433° P RACTICE P ROBLEM #2 A hiker walks 80 m North, 20 m East, 50 m South, and 30 m West. What is the magnitude and direction of the hiker’s displacement? By subtracting the opposing directions from each other, we find the hiker’s displacement along the y-axis to be 30 m North, and the displacement on the x-axis to be 10 m West. a2 + b2 = c2 302 + 102 = R2 R = √900 + 100 R = 31.623 m tan θ = opp/adj θ = tan-1 (10/30) θ = 18.435° AIM – What are the components of the resultant? DO NOW – A car drives 4 miles North, 3 miles East, and 2 miles South, what is its total displacement? HW - Textbook p. 53 #50, 51, 53 V ECTOR A DDITION V ELOCITY V ECTORS Occur at the same time – concurrent Displacement vectors occurred sequentially – one after the other Boat velocity Boat Stream velocity River How do we find the resultant velocity? Resultant velocity found by drawing the vectors head to tail – just as with displacement 8 m/s Boat Boat 6 m/s 8 m/s θ 6 m/s VR Velocity Resultant VR2 = 82 + 62 = 100 VR = 10 m/s tan θ = 6/8 θ = tan-1 (6/8) = 37° V ECTOR C OMPONENTS If R = A + B, then we can say that A and B are components of R Two or more components add to make a resultant A resultant can also be resolved back into components!! B R A Rectangular Components – components which lie on the x and y axes J APANESE V ECTOR V IDEO Japanese Vector Video - Launching a Ball from a moving truck