What word do you use when you are trying to say that you attempted to do or solve something which you know would most probably fail?
For example, I dropped my Nokia off the highest level of the Eiffel Tower. The screen shattered and the phone could not be turned on anymore. In a [word] attempt, I still tried to repair the phone.
In that example, I am not feeling reluctant. I know it's almost impossible to fix that phone but I'm still giving it a shot. What is the word or feeling that I should use?