synonyms: throw, toss, fling, pitch, hurl, lob; informal chuck "he cast the stone into the stream"
The word give means to give something away and it sounds very passive or non-aggressive. I don't the we get the full meaning with this word. And we do not appreciate what the Lord is saying to us.
The word cast means to fling and it has an interest meaning: it means to throw forcefully. This is definition is aggressive.
The word cast can also mean to hurl which also means to throw forcefully - aggressive.
The word cast also means to chuck which means to throw something away because you don't want or need it any longer. This word is both passive and aggressive.
In this analogy we are the quarterback and life if come at us head on wanting to tackle because we are carrying the ball (burdens and cares). Jesus is the wide receiver and He is waiting in the end zone for us to throw our ball (burdens and cares) to Him. Once He has received the ball (burdens and cars) in the end zone the play is over. "TOUCHDOWN!", The crowd cheers!
We cannot pickup the ball again and run with because the play is no longer ours.
The image is from Bible.com and I think it completely illustrates how we are to cast our cares and burdens to the Lord. Throw your burdens, your cares, your worries towards heaven. Jesus is waiting to receive them as all heaven rejoices when He received them. You have successfully thrown away those burdensome cares that have weighed you down. You will no long try to pick them up because your hands are lifted up towards heaven instead of downward. You hands are now throwing praise and worship up to heaven. All heaven is glorifying the Father because of what you trust Him with all your cares, burdens, and worries.