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Introduction to Head to Tail Vector Addition

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Basics of Head to Tail (Tip to Tail or Graphical) Vector Addition

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good morning today we're going to increase our knowledge of tip to tail vector addition by slightly altering our example involving anybody track that are slow velocity racing here we go last time we had slow Lost Sea racer racing parallel to the moving track to make things a little more interesting we're going to increase the width of the movie track racer can race at 42 millimeters per second now let's take a look at the moving track to measure the displacement and time for the determine the velocity of the North Myrtle Beach you can see the track move 0.60 meters North or 600 North in 12.2 seconds the velocity of the track equation for velocity velocity equals displacement over change in time Billy what was careful displacement is a vector and 600 mm is just the magnitude of the displacement of the directions to 600 North so the velocity of the race car ends up being 600 North divided by 12.2 seconds or 49.180 for approximately 49 millimeters per second North the velocity vectors for the track and slow velocity race car mathematically are like this just so you know it should be pretty clear from the video that these glasses are not perfectly constant us or just me use two significant digits on these velocities now I know it's not perfect but it's good enough for our demonstration today at the school budget is pretty tight right now It's All About the Benjamins baby velocity Vector is going to be represented by this Capital with an arrow over the top capital B is a vector inbox your seed in boldface type lawsuit see if with the arrow over the top on the board so I will always be using the era so the race car has a velocity Vector with a magnitude of 42 millimeters per second ending direction of East the track is Illustrated with a velocity Vector Capital again with the arrow over the top so the track has a magnitude of 49 m per second and a direction of North why doesn't really matter I just took the first two letters of the alphabet really you can pick whatever letters you would like to do now is figure out what are slow Blossom race cars velocity would be if she were to race on the track so it's going to be vector addition and I'm going to draw it's like on the board map so this is Factor XA for the northward we track and this is Vector for the East removing race car and that could be used this long so that they both have a lamp which matches the magnitude of those vector call tip to tail vector addition because the tip of a vector a is on the tail of a vector B eraser races on the track can you come see when we add the 49 millimeters per second North to the 42 rickets mobile RC Racers new velocity which we can illustrate on the board like this and you can see that this Factor are illustrates exactly how she ends up moving on the truck leaders find the results of adding vectors A and B together what we get is called the resultant Vector r in this particular case our resultant Vector is flow velocity race cars resultant velocity from racing on the track how we going to find this resultant Vector we should just be able to use a squared plus b squared equals c squared what is it about this triangle that tells us we can use them because Northeastern music a right triangle so now we can find a resultant vector substituting indoor equation we get the resultant Vector squared is equal to Vector a square + vector Square √ outside to get the results numbers we get the results to the square root of 49 squared + 42 squared 4.537 or 2 sig figs 65 millimeters per second in other words slow loss erasers resultant velocity Vector is 65 m per second Americans have both magnitude and Direction velocity is a vector so we need to figure out slow blast erasers directions as well Siri search results in Pulaski however we also need to figure out the direction in or the resultant velocity Vector of a race car Billy Howell another word for we going to figure out this angle call Mama, right triangle so we can use it Alzheimer's not fun for today. You are not alone often students forget beta it makes me sad every time opposite of our angle Theta is the vector and I Jason's to our angle Theta is Vector a has a magnitude of 42 and 9 4910 Chabot Science we get back over 49 which works out to be as 40.601 or 41 with 2 sig figs show me independently figured out the magnitude and the angle for the resultant velocity of our race car which means the resultant velocity Vector works out to be with two significant digits millimeters per second at an angle of 41 degrees east of north east of North absolutely okay at this point in our next lesson how to work with cardinal directions in physics so what is Tagamet and review exactly what this mean went slow balasi racer races at 42 millimeter on a track that is moving at Pokemon go she will actually be traveling at 65 m m at an angle of 41 degrees east of North because 49 millimeters per second North + 42 millimeters per second East equals 6 41 degrees east of North pull up mr. I think maybe I'm confused or I'm missing something to add 49 + 42 + 65 91 awesome question how can 49 + 42 equals 65 exactly answer to question is that your question is wrong question 49 + 42 49 + 42 what is she was a weird vectors not stay lit so he doesn't work this make any sense if you just drop the directions so Northwest 42 millimeters per second equals 65 set an alarm for here we add vectors it just doesn't make sense 49 + 42 definitely does not equal 65 however 49 millimeters per second North + 42 millimeters per second East does equal with two sig figs 60 millimeters per second at an angle of 41 degrees east of what was going to go over that weird east of North next time next lessons a quick review tip to tail back illustrate that usually on the board using arrows of the correct length we did that using letters with an arrow over the top of the street that they are vectors because we had a right triangle we could use the potty answer to figure out both the magnitude and the direction of a resultant velocity vectors vector vector good with me today I enjoyed learning with you

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Introduction to Head to Tail Vector Addition

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