1 / 14

Vector Addition

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.

ryu
Download Presentation

Vector Addition

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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

  3. 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!!

  4. 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

  5. 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°

  6. Vector Addition (cont.) Same Direction: simply add = 11 m 4 m 7 m Opposite Direction: subtract 5 m = 4 m 9 m

  7. 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?

  8. 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°

  9. 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°

  10. 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

  11. 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

  12. 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

  13. 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!!

  14. Japanese Vector Video Japanese Vector Video - Launching a Ball from a moving truck

More Related