Consider a velocity field with

$u=y+t$

$v=sin(t)$

$($a$)$ Find the streamline that paths through point $(1,1)$ at different times.

$($b$)$ Determine the path line of a particle which was at $(1,1)$ at time $t=0.$

$($c$)$ Find the streak line of point $(1,1)$ at time $1.$

$($d$)$ Evaluate the deformation rate tensor and vorticity vector in this flow field.