A disc of radius R starts at time `t=0` moving along the positive x-axis with linear speed `v` and angular speed `omega`. Find the x and y coordinates of the bottom most poitn at any time `t`.

Options

A. `(x,y)-= (vt-R sin omegat,R-R cos omegat)`
B. `(x,y)-= (2vt-R sin omegat,R-R cos omegat)`
C. `(x,y)-= (vt-R sin 2omegat,R-R cos omegat)`
D. `(x,y)-= (R sin omegat,R-R cos omegat)`

Explanation

At time `t` the bottommost poit will rotate and angle `theta=omegat` with respect to the centre of the disc C. The centre C will travel a distance `s=vt`.
In the figure, `PQ=Rsintheta=Rsinomegat` and `CQ=Rcostheta=Rcosomegat`
coordinates of point P at time t are `x=OM-PQ=vt-Rsinomegat`
and `y=CM-PQ=R-Rcosomegat`
`therefore(x,y)=(vt-Rsinomegat,R-Rcosomegat)`