cast off vs give someone the push

cast off

verb
  • To discard or reject something. 

  • To let go (a cable or rope securing a vessel to a buoy, wharf, etc.) so that the vessel may make way. 

  • To finish the last row of knitted stitches and remove them securely from the needle. 

  • To estimate the amount of space required by the type used for the given copy. 

give someone the push

How often have the words cast off and give someone the push occurred in a corpus of books? (source: Google Ngram Viewer )