A particle is moving in a plane with velocity given by `vec(u)=u_(0)hat(i)+(aomega cos omegat)hat(j)`, where `hat(i)` and `hat(j)` are unit vectors along x and y axes respectively. If particle is at the origin at `t=0`. Calculate the trajectory of the particle :-

Options

A. `y= a sin (u_(0)/(omega x))`
B. `y= asin ((omega x)/u_(0))`
C. `y=1/a. sin (u_(0)/(omega x))`
D. `y=1/a. sin((omega x)/u_(0))`

Answer

B

Explanation

`u_(x)=u_(0), u_(y)=a omega cos omegat`
`x=u_(0)t, underset(0)overset(y)(int)dy=aomega underset(t=0)overset(t)(int) cos omegat dt`
`y=aw/w sin omegat=a sin ((omegax)/u_(0))`