Mr. Rockensies – Regents Physics V ECTOR A DDITION 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 ECTORS 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

D RAWING V ECTORS Vectors can be drawn to graphically represent magnitude as well as direction. θ Horizontal Axis = +X direction length NEVER FORGET TO DRAW THE ARROWS!! Length indicates magnitude, and therefore must be drawn to scale using a ruler and protractor. The angle indicates direction, represented by θ (theta).

R ESULTANT – A DDING V ECTORS Resultant – the result of 2 or more displacements (vectors) 20 m North 20 m West R θ R = resultant displacement θ = direction 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: 20 m North 20 m West R θ R 2 = (20m) 2 + (20m) 2 R = √ 800 m 2 R = 28.2 m a 2 + b 2 = c 2 tan θ = opp/adj = 20/20 = 1 θ = tan -1 (1) = 45°

V ECTOR A DDITION ( CONT.) Same Direction: simply add 4 m7 m = 11 m Opposite Direction: subtract 5 m 9 m = 4 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?

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? 1500 miles 200 miles Resultant miles a 2 + b 2 = c 2 (1500 m) 2 + (200 m) 2 = R 2 R = √ (1500 m) 2 + (200 m) 2 R = m θ tan θ = opp/adj θ = tan -1 (200/1500) θ = ° **not drawn to scale**

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. a 2 + b 2 = c = R 2 R = √ R = m tan θ = opp/adj θ = tan -1 (10/30) θ = °

Mr. Rockensies – Regents Physics V ECTOR A DDITION 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 ELOCITY V ECTORS Occur at the same time – concurrent Displacement vectors occurred sequentially – one after the other Boat Boat velocity Stream velocity River How do we find the resultant velocity?

Resultant velocity found by drawing the vectors head to tail – just as with displacement Boat 8 m/s 6 m/s 8 m/s 6 m/s θ V R Velocity Resultant V R 2 = = 100 V R = 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 B A R Two or more components add to make a resultant A resultant can also be resolved back into components!! 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