A particle moves in a plane according to the law v=v0*i+b*omega*cosomega*t*jIf the particle is at origin at time t=0, determine the equation of the...

The formula for the vector of velocity
is:

v = vx*i +
vy*j 

We'll identify the projections of velocity form the
formula v=v0*i+b*omega*cosomega*t*j:

- x axis
projection:

vx =  dx/dt =
v0

dx = v0dt

Int dx = Int
v0dt

x = v0*t + C

t = x/v0
(1)

- y axis projection:

vy =
dy/dt = b*omega*cos(omega)*t

dy = b*omega*cos(omega)*t
dt

Int dy = Int b*omega*cos(omega)*t
dt

y = b*t*sin(omega) + C
(2)

We'll substitute (1) in
(2):

y =
b*(x/v0)*sin(omega)

If t = 3pi/2*omega => x =
3pi*v0/2*omega

y =
b*(3pi*v0/2*omega*v0)*sin(omega)

y =
b*sin(3pi/2)

y = b*(-1)

y =
-b

The distance of the particle from the
origin is:

r = sqrt(x^2 +
y^2)

r = sqrt[9(pi*v0)^2/4*omega^2 +
b^2]