To throw down/throw out (to toss something forcefully); also to stretch out one's legs (e.g. sit and stretch legs).
彼は書類を机の上に投げ出した。
He threw the documents onto the desk.
疲れてソファに座り、足を投げ出した。
Tired, I sat on the sofa and stretched out my legs.
子供が玩具を床に投げ出して泣きだした。
The child threw the toy onto the floor and started crying.
To abandon or give up (a task or responsibility); to quit or walk out (e.g. resign or leave someone/stuff unfinished).
彼はプロジェクトを途中で投げ出してしまった。
He gave up on the project halfway through.
問題が難しくなるとすぐ投げ出すのではなく、最後までやり抜きなさい。
Don't give up as soon as things get hard; see it through to the end.
あの支店長は責任を投げ出して逃げたと噂されている。
There's a rumor that the branch manager abandoned his responsibilities and ran away.
To give freely or sacrifice (e.g. one's life or body) for others; to throw oneself into an action in a self-sacrificing way.
彼は仲間を守るために身を投げ出した。
He threw himself into protecting his comrades.
その兵士は国のために命を投げ出したと称えられた。
The soldier was praised for sacrificing his life for his country.
To start to throw; to begin a throwing motion (i.e. the act of beginning to toss something).
彼は合図とともにボールを投げ出した。
At the signal, he began to throw the ball.
子供たちは砂場で砂を投げ出して遊んでいた。
The children started throwing sand while playing in the sandbox.