Unsteady Fluid Flow: Incompressible and Stream Function Calculation

[ra_forever8]

An unsteady fluid flow has velocity field q= - 1/2 sin t ( xe^-y, e^-y).
Show the flow is incompressible and find a stream function.
Find the path of the fluid particle which is at (1,0) at t=0.

I only know it has six faces and the sum of all six terms has to be zero in order to show the flow is incompressible.
Rest i really don't how to slove the problems

 

[Chestermiller]

Were you taught that, if the flow is incompressible, then the divergence of the velocity vector must be equal to zero? Do you know the formula for calculating the divergence of a vector?