superimposing vector and raster data

I have created a Python code that uses:
a. a grid file of water depth values in a region (Every cell is 10x10 m) and
b. a polygon shapefile of land use information

Generally the code reads the depth values in every grid cell and according to the land use of each cell performs several calculations

And now here comes the problem:

At first I made the assumption that the land use found in the center of every grid cell represents the land use of the whole cell.

But I am wondering whether a big error takes place in cells which cover two different land use polygons.

Is it worthy to find a way to calculate the irregular areas that come up in those grid cells, which “carry” the same landuse information? Or I should only minimize the dimensions of every grid cell (to 5x5 for example), minimizing in this way the error?

Thank you very much for your time!