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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). Vector Addition. Mr. Rockensies – Regents Physics. Vectors. Quantities with magnitude (amount, size) and direction.
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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) Vector Addition Mr. Rockensies – Regents Physics
Vectors Quantities with magnitude (amount, size) and direction. Example: 20 m North or 20 m West Vectors Displacement Velocity Acceleration Scalars (no direction) Distance Speed Time Mass
Drawing Vectors 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. The angle indicates direction, represented by θ (theta). length θ Horizontal Axis = +X direction NEVER FORGET TO DRAW THE ARROWS!!
Resultant – Adding Vectors Resultant – the result of 2 or more displacements (vectors) 20 m West R = resultant displacement θ = direction 20 m North R θ R = 28 m, 45° determined by measuring with a ruler and protractor
Mathematical Techniques 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 = √800 m2 R = 28.2 m 20 m North R θ tan θ = opp/adj = 20/20 = 1 θ = tan-1 (1) = 45°
Vector Addition (cont.) Same Direction: simply add = 11 m 4 m 7 m Opposite Direction: subtract 5 m = 4 m 9 m
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?
Practice Problem #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 Resultant - 1513 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°
Practice Problem #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 Vector Addition Mr. Rockensies – Regents Physics
Velocity Vectors Occur at the same time – concurrent Displacement vectors occurred sequentially – one after the other Boat velocity Boat How do we find the resultant velocity? Stream velocity River
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 VR2 = 82 + 62 = 100 VR = 10 m/s tan θ = 6/8 θ = tan-1 (6/8) = 37° θ 6 m/s VR Velocity Resultant
Vector Components If R = A + B, then we can say that A and B are components of R B R Two or more components add to make a resultant A Rectangular Components – components which lie on the x and y axes A resultant can also be resolved back into components!!
Japanese Vector Video Japanese Vector Video - Launching a Ball from a moving truck