anonymous
  • anonymous
Help please!!!!(: A wall clock has a minute hand with a length of 0.56 m and an hour hand with a length of 0.23 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x axis pointing to 3 o'clock and the positive y axis pointing to 12 o'clock. Write the vector that describes the displacement of a fly if it quickly goes from the tip of the minute hand to the tip of the hour hand at 3:00 P.M. (Let Dvec represents the displacement of the fly.) Vector D=_____m(i-hat)+_____m(j-hat)
Physics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@ganeshie8
theEric
  • theEric
Hi! So it looks like you want the answer in the for of \(\vec D = a\hat i+b\hat j\). How familiar are you with vectors?
theEric
  • theEric
@pdd21

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes! and how to do it lol @theEric
anonymous
  • anonymous
i'm somewhat familiar with vectors.
theEric
  • theEric
Okay! Well, that's a good start! :) You have a coordinate system laid out by the clock, where the \(x\) and \(y\) axes run through the center, where the \(y\)-axis goes up to the 12 spot and \(x\)-axis goes right to the 3 spot. Drawing a picture is usually helpful!|dw:1378786394707:dw|
theEric
  • theEric
There is your coordinate system!
theEric
  • theEric
Cartesian just means we're talking about \(x\) and \(y\) rectangular stuff.
theEric
  • theEric
Now we want to look at the hour and minute hands - to continue building up this picture. I will draw \(\sf vectors\) that point to the \(\sf ends\) of the hands, because that describes the two \(\sf positions\) of the fly. That is important, because the \(\sf displacement\) you seek is the \(\sf change\ in\ position\), from the end of the minute hand to the end of the hour hand.
anonymous
  • anonymous
okay
anonymous
  • anonymous
i'm following so far(:
theEric
  • theEric
|dw:1378786720213:dw| Those vectors point to the \(\sf position\) of the ends of the hands! The hour hand is the shorter one, pointed at three. There are no extra minutes, so the minute hand is at 12!
theEric
  • theEric
I'm glad! Thanks for letting me know! :D
theEric
  • theEric
Now, I'm guessing you are used to expressing vectors with \(\hat i\) and \(\hat j\) - unit vector notation. So, what would the vector to the end of the minute hand be? What about the vector to the end of the hour hand?
theEric
  • theEric
(I'll give you hints if you need.)
anonymous
  • anonymous
so i-hat would be the x-axis right? and j-hat is the y-axis. the end of the hour hand is 3? and the end of the min hand is 12?
theEric
  • theEric
Right, right, right, and right. How it works, then, is that \(\hat i\) is a unit vector in the \(x\) direction. When you multiply anything to it, say \(a\), the result is a new vector, where the length is changed based on \(a\)! So, adjusting \(a\), you can have any length of the \(x\) direction vector. That covers your \(x\) component. Then, for your vector's \(y\) component, you have your \(\hat j\), which works the same way but in the \(y\) direction. Sometimes you combine these components with "vector addition," which makes the result equal a vector that has both \(x\) and \(y\) components, and so it looks slanted!|dw:1378787354562:dw| Now, in your case, these two hands line up with the axes, so you don't have two combined components for either of them.
theEric
  • theEric
The direction will come from whether you use \(\hat i\) or \(\hat j\). The magnitude will come from what you multiply the \(\hat i\) or \(\hat j\) by. The magnitude should be the length of the hand you're making a vector for. Those lengths are given in the problem, and I drew them into one of my pictures.
theEric
  • theEric
So, What might a good vector be to describe the position of the end of the hour hand?
anonymous
  • anonymous
(0.23)(3)m(i-hat)?
anonymous
  • anonymous
0.69m(i-hat)
anonymous
  • anonymous
I'm pretty confused on this part hah
theEric
  • theEric
Close! The number "3" just indicates where the hand is pointing - in direction from center to 3 - so it's not a part of your magnitude. Leave it as \(0.23\hat i\) and you're fine! :) Just to get you used to labels, I'll say that that is \(\overrightarrow {D_h}=0.23\hat i\), where \(_h\) indicates it's the hour hand vector. Now what about \(\overrightarrow {D_m}\), the minute hand's end's position vector?
anonymous
  • anonymous
Ohhh, I though it would be much more difficult haha, 0.56(j-hat)???
theEric
  • theEric
Haha, no, you got it! And you got it again! :) Now what's left? The displacement, or change in position. That's what's left. That is a little tricky. First if you want to find the difference between numbers, what do you do? You subtract. The distance from \(4\) to \(5\) is \(5-4=1\). So, what about vectors? Same thing. It does work out. The change from \(\overrightarrow {D_m}\) to \(\overrightarrow {D_h}\) is \(\overrightarrow {D_h}-\overrightarrow {D_m}=\overrightarrow D\). Now, do you know what to do for vector subtraction?
anonymous
  • anonymous
0.56(j-hat) was apparently wrong.... so 0.56-0.23?
anonymous
  • anonymous
@theEric
theEric
  • theEric
\(0.56\hat j\) in meters should be correct for the end of the minute hand, but that is not the answer you seek. The subtraction is \(\overrightarrow {D_h}-\overrightarrow {D_m}=\overrightarrow D\). \(\overrightarrow {D_h}=0.23\hat i\) \(\overrightarrow {D_m}=0.56\hat j\) Substitution yields... Do you want to fill it in, maybe?
anonymous
  • anonymous
so D would be -0.33
theEric
  • theEric
\(\overrightarrow D=0.23\hat i-0.56\hat j\) And, that's the format you want for your answer! Don't forget that \(0.56\) multiplies \(\hat j\), while \(0.23\) multiplies \(\hat i\). Just like with algebra, you can't add terms that are multiplying different variables! It's a lot like \(0.56c+0.23d\).
anonymous
  • anonymous
Ohhhhhh,,, that makes much more sense! haha
theEric
  • theEric
Yeah! And that's all that there is to it! Vector addition and subtraction aren't too bad in unit vector notation after you get to know them! :) Congrats!
anonymous
  • anonymous
Thank you so much! Could you by chance help me with two other problems i've been having a hard time with?
anonymous
  • anonymous
@theEric
theEric
  • theEric
Actually, I really have to get going to bed... If you post one as a separate question, then maybe someone else will see it and help with it! I can look at it quick, and tell you which concept to look at, but I really have to sleep soon.

Looking for something else?

Not the answer you are looking for? Search for more explanations.