throw, discard, abandon, launch into, join, invest in, hurl, give up, sell at a loss
投 centers on sending something away from oneself with force or intention: throwing, hurling, discarding, or abandoning. Extended senses like launching into an activity, joining, or investing in something share the idea of directing oneself or resources outward, while selling at a loss is a financial abandonment.
contribution (to a newspaper, magazine, etc.); submission; post (on a blog, social media, etc.)
voting; ballot; poll; vote
investment
throw; throwing
throwing in; inserting; depositing (e.g. a ballot)
pitcher
throwing down; dropping; airdrop
to throw; to hurl; to fling; to toss; to cast
administration (of medicine); giving medication
projection (of a shadow); casting (a reflection); reflection; cast shadow
pitching; throwing a ball; bowling (in cricket); pitched ball
surrender
abandonment; giving up; throwing away; disposal; dumping
pitching in consecutive games
administration; medication; dosage
speculation; venture; stockjobbing; gambling (on stocks)
to throw; to cast (e.g. vote, light, shadow)
mailing; posting
going the whole distance; pitching a whole game
investment trust
good (nice) pitching
stone throwing
projection (of an image)
letter (e.g. of complaint); letter to the editor; letter from a reader
投 combines 扌 (hand) with 殳, a component associated with striking or action. The character likely expresses the idea of throwing or casting with the hand.
The left side is a hand 扌, and the right side 殳 suggests a striking tool. Picture a hand throwing a tool or weapon, sending it flying away.
For トウ, imagine throwing a toe-shaped object: toe -> トウ, and your hand hurls it across the room.