It's just a combination. :)
- woord = word
- antwoord = answer
- verantwoord = responsible^
- verantwoordelijk = responsible^
- verantwoordelijkheid = responsibility
^ verantwoord means responsible in the general sense, verantwoordelijk means someone or something specific is responsible for something (or caused something):
- het is verantwoord om kinderen hiernaar te laten kijken = it is responsible to let children watch this
- het is onverantwoord door de onweersbui te fietsen = it is irresponsible to bike through the thunderstorm/lightning
- hij is verantwoordelijk voor het eten = he is responsible for the food
- het hogedrukgebied is verantwoordelijk voor het lekkere weer = the high pressure zone is responsible for the good weather
- het is mijn verantwoordelijkheid om dat te bepalen = it is my responsibility to decide that
While it may be too obvious to state, it is handy also to remember that the root of "responsible" is "response", which is "answer."
You are responsible or verantwoordelijk for something if you can answer for it. "If this project fails, you will answer for it." (You are responsible for it.)
Indeed, the English word "answerable" means "obliged to answer or be called to account." We just don't use it much.