A particle is moving in a plane with a velocity given by. the particle is at the origin at t=0. he trajectory

a particle is moving in a plane with a velocity given by -
U = u i^(i cap) + wa cos(wt) j^ (w=omega and a =accelaration)
. the particle is at the origin at t=0. the trajectory of the particle is?
a)y = a sin(wu/x)
b)y = a sin (wx/u)
c)y = a cos(wu/x)
d)y = a cos (wx/u)
hint - answer is option B. Can someone please help me out?
thanks

The velocity in the y direction is given as ωa cos ωt

dy /dt = ωa cos ωt

Integrating

y = a sin ωt + C
Using the condition that y = 0 when t = 0

C = 0

Hence y = a sin ωt
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From dx/dt = u

dx = u dt

Integrating x = ut + c

Using the condition that x = 0 when t = 0

x = ut and hence t = x/u

y = a sin ωt = a sin (wx/u)

hence the answer is b) y = a sin (wx/u)


C = 0

Hence the answer is y = a sin ωt