A particle of mass m moves with a force varying with velocity as F=a(yi - xj), a is a positive const, and i & j are unit vectors along x and y axes. At the initial moment(t=0), the particle was located at x=y=0, and had a velocity Vo directed along the unit vector j. Find the law of motion x(t), y(t) of the particle, and also the equation of its trajectory

 

can anybody plz tell wat im doing wrong

 

my answer:

F=ayi - axj

a=ay/m i - ax/m j

 

Ax=ay/m  (acc in x dir)

Ay=-ax/m ---- 2 (acc in y dir)

 

substitute x=Asinwt in 2

integrate 2,

we get Vy=aAcoswt/wm

at t = 0,

Vo=aA/wm

or A=vo/w   (where w²=a/m)

 

and let y=Bsinwt

therefore Vy=bwcoswt

Vy=w(B²-y²)^1/2

or Vo = wB (substituting initial conditions)

 

now we have A and B,

on squaring and adding, we get

x² + y² = (Vo/w)²

 

but the answer given is (x-vo/w)² + y² = (Vo/w)²

 

 

can anyone please tell me what im doing wrong...

 

rates assured