**** Etymological explanation
- 無理： 理が無い（ので達成できない）
you can't acieve it because it is unreasonable
- 駄目： it makes no difference (やっても無意味、無価値）
This word originates from GO (囲碁) game,
駄目 in 囲碁 means "useless/worthless slot", which turns to mean simply "useless/worthless".
However, nowadays 駄目 is often used to express prohibition, "Don't do that"
you usually use むだ to express "worthless/useless even if you try".
このプールは深いから、子供が泳ぐのは無理だ。: A description with a reason.
Children can't swim here because they are small but the pool is deep.
このプールは深いから、子供は泳いじゃダメ : A prohibition
Children is not allowed to swim here because it is dangerous.