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In this assignment, you have three questions that are all dealing with vectors, and we'll take each one at one at a time.
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So the first question, they give you a vector a magnitude 80 meters per second, 25 degrees east of south.
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I'll be drawing these out in a second.
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Then they tell you about this other vector that it's 1 .5 times a.
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I call that b.
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I'll call that b.
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Now, what does this mean 1 .5 times a? this is a vector notation here.
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Well, he has two things.
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Same direction as a, since the factor multiplying the vector a is positive, since 1 .5 is greater than 0.
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So it's in the same direction.
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And second, the magnitude of b is 1 .5 times the magnitude of a.
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And we can write this without the arrow signs b equals 1 .5 times a.
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So with a positive multiplying factor, you're in the same direction, and you're the magnitude length, if you like, even though they're using length in this problem a little differently because they talk about drawing it on paper.
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So let's leave that alone.
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Let's just call it magnitude of b is 1 .5 times the magnitude of a.
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So let's draw these out, see what it looks like.
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So here is a, it just arbitrary length.
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We'll get into the actual scale unit, scale length in a second.
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There's a, this angle here, this angle here is 25 degrees, east of south.
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So the first word tells you what to do relative to the second word.
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South is the base, and you're east of that.
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West of south would be over here.
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It would be over here.
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Okay, so there's a.
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Now b is 1 .5 times that.
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Actually, let me change the color.
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So you can see it a little better.
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Even though i can't draw straight line very well.
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That's not too bad.
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1 .5.
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That's b.
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Same factor direction.
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But 1 .5 times the length.
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Okay.
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Now we'll get back to angles in a second.
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Now let's use the scale factor.
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So if you were going to do this precisely on paper, graphically, they want to scale of one centimeter, of course, one centimeter on that paper corresponds to the physics 10 meters per second.
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That's what you're trying to describe, but we've got to have some scale on the paper.
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And so this is on the paper, and this is what's given to you as a vector.
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So, this is really like a unit conversion.
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1 .5 times 80 meters per second times.
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So this would give you, this gives you a certain amount of, well, this is 120, obviously meters per second for b, then we want to scale this for the paper.
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One centimeter.
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So like i said, it's like you're going from meters per second to scale units, paper units, if you like, conversion like that.
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So one centimeter, and meters per second.
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So notice the meters per second cancel out, you're left with centimeters.
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So really, what's different about this than doing those chain link conversions with units.
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Nothing.
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So this is 12 centimeters.
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So you'd have to take out your ruler and draw 12 centimeters at an angle 25 degrees from the south.
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So we have b is 12 centimeters on the paper.
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But now we've got to do our angles.
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Now they want it from the plus x axis.
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So this.
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So you can go, you could possibly have the counterclockwise angle or you could have the clockwise angle.
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Or you could have the clockwise which would be negative so if we go around counterclockwise this would be 270 degrees plus 25 degrees remember this is 90 180 270 so this would be 295 degrees if you were to go around clockwise you'd be minus 90 degrees minus 25 degrees minus 65 degrees minus 65 degrees now our choices though that's not one of them but this is so at 295 degrees this is our answer so this is choice b choice b in your choices so those are only you know only two possibilities either counterclockwise or clockwise in terms of that so that was question number that was question number five question six now a hundred meters per second south that's the vector b this time minus 0 .8a 0 .8a so based on what i've said minus sign implies an opposite direction opposite direction of a and we also have b is equal to 0 .8 a whatever that absolute value of that multiplying factor is that's how you scale the magnitudes.
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Done deal.
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The plus or minus will tell you do you have the same direction or do you flip it? that's the only choices.
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It's the only choices.
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So if we draw this out, we draw this out and actually let me see and i got along the axis.
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There's going to be a and a b.
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So almost the same length of a.
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But notice the exact opposite, exact opposite direction.
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A is south, b is north.
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This angle here is 90 degrees.
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Now, you could actually, this one here, even though it's not a choice, you could actually 90 degrees, remember, positive angles are counterclockwise, negative angles are clockwise.
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Or you could actually have the minus 270.
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That one's not a choice.
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These are all 90s.
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So again, we use the same scale, one centimeter, 10 meters per second.
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This is for drawing on the paper.
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So 0 .8, 100 meters per second times one centimeter, 10 meters per second, 8 centimeters.
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So we have that b is 8 centimeters at 90 degrees.
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So this is choice d.
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So those are just having to explore what it means to have one vector formed from another by multiplying it by some type of scalar quantity.
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Scalar meaning a number, positive, negative, or zero.
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Not a vector, just a number.
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Okay.
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Question seven.
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We're given two vectors, a, 10 meters west, b, five meters north.
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And you're supposed to add those.
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Find out.
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Don't have to be doing it precise.
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You don't have to be doing it with any type of trigonometry or geometry or anything like that...