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jauneet singh Grade: 12
        the velocity of the particle noving in the x-y plane is given by dx/dt=8asin2at,dy/dt=5acos2at.when t=0,x=8andy=0,the path of the particle is a.................here a=3.14

sir plz tell some 2 way to find path of particle
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear jauneet


to find the path means you have to find the ralation ship between x and y with the given information .


here we have to eleminate the t .


dx/dt=8asin2at


intigrate


 x= -(8acos2at )/2a   + c1


 x = -4cos2at + c1


now use the given condition


at t=0 ,x=8


so 8=-4 +c1


 c1=12


 so equation become


x =-4cos2at + 12 


or  (x-12)/4 = -cos2at ............1


now similerly for y


dy/dt=5acos2at


intigrate


y= (5asin2at)/2a  +c2


y =5/2 sin2at + c2


now apply condition


y=0 at t=0


0 =0+c2


c2=0


so equation become


y =5/2 sin2at


or 2y/5 = sin2at ............2


 


now square equation 1 and 2 and add


((x-12)/4)2 + (2y/5)2 = 1


this the path of the article


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Badiuddin




7 years ago
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