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![[Post New]](/templates/default/images/icon_minipost_new.gif) 22 Nov 2007 17:20:51 IST
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A particle is moving in a plane with velocity given by: v=ui+(  acos t)j. (i and j are unit vectors along X and Y axes.) If it is at origin while t=0,calculate trajectory. At time 3pi/2 find its distance from origin. (Its quite straightforward,but I'm stuck at one step!!)
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22 Nov 2007 18:15:26 IST
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*edited*
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Will nip in at times to solve problems :)
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22 Nov 2007 18:23:01 IST
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tell me if distance from origin at t = 3pi/2w is 0.. , learner?
ill post then.
g2g bye
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22 Nov 2007 18:36:13 IST
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hey karthik, here frame of reference is not mentioned then how can you take acc. = g........????????
it is a direct problem, can be solved using caculus
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LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
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22 Nov 2007 18:42:44 IST
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vx=u so dx/dt = u integrating we get, x=ut+c vy=wacoswt so dy/dt =wacoswt integrating, y=asinwt + k since at t=0, x=0 and y=0 so c=k=0 x=ut or t=x/u y=asin(wx/u) is the trajectory
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22 Nov 2007 18:45:29 IST
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I think answer should be
x = 3(pi)u/(2w), y = -a
and equation of trajectory shold be
y= asin[wx/u]
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my future signature:
LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
Albus Dumbledore
Harry Potter and the Prisoner of Azkaban movie
There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
-- Albert Einstein
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22 Nov 2007 18:51:01 IST
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and distance from origin= sqrt(x^2 + y^2)
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my future signature:
LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
Albus Dumbledore
Harry Potter and the Prisoner of Azkaban movie
There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
-- Albert Einstein
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22 Nov 2007 18:52:32 IST
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from your given data. I calculate something and i get that. X= 3  u/2 ...... Y= {9 2aCos }/{8 }......... here we get that R = sq.root of {x2+y2} = distance between origin. R= 3pi sq.root {4u2+9pi2a2cos2w}/{4w} If w is constant then R is constat then it's trajectory is st.line.
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22 Nov 2007 19:10:20 IST
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No,spidey,its not zero...thats the second part. @Karthik,I dont think its a projectile(frame of reference not being mentioned),so I'm not sure if you can use g...but your value for x is right. @rhd...and lokeshsardana..the equation you gave is correct. My doubt was:dy/dt=wacoswt...how to proceed from there... I didnt think of integrating-stupid of me  .(not to mention I'm not good at it-just learning!!) Btw,the answers you finally get are:Path:y=asinwx/u. Distance:sqrt(9pi^2u^2/4w^2+a^2) Thanks everyone!!
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22 Nov 2007 19:10:56 IST
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sorry, my mistake post edited............
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my future signature:
LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
Albus Dumbledore
Harry Potter and the Prisoner of Azkaban movie
There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
-- Albert Einstein
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22 Nov 2007 20:27:27 IST
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@learner - if you want, you can use the method of calculus as well. You know the components of velocity, so obtain x and y co ords, and use distance formula
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Will nip in at times to solve problems :)
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22 Nov 2007 20:35:31 IST
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dffggfgfgf
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22 Nov 2007 20:38:53 IST
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yup...I think thats the only way to do it,right? all the correct solns i saw were using that itself.. thanks!!
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22 Nov 2007 23:11:19 IST
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Yeah, and that would be the easiest method as well
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Will nip in at times to solve problems :)
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