Science is always going to try to attempt to answer "unanswerable" questions. Scientists have answered questions like this and have succeeded and made tremendous, groundbreaking discoveries. Science is always moving forward and new discoveries are being made every day. If scientists stop exploring possibilities and jumping into the unknown then science as we know it will come to a screeching halt.
This is a good question. Here are a few perspective to consider. First, unless people research a topic, people will not know if something is answerable or unanswerable. Often times, people find answers to things that seemed impossible. Second, science has progressed so much and if you are able to stand on the shoulders of others, then you might be able to achieve more and more. With this hope, people strive to answer even "unanswerable things." Third, I think there is a certain amount of hubris involved in science. Science thinks it can answer anything, when if fact it probably cannot. Thomas Khun and Peter Berger has written some great things on science and the myth of continual progress.
Even if we never find the answer to some of these questions, the pursuit of such answers often yields unexpected dividends. There are many things we may never be able to explain or understand about space and the origins of the universe, but through our attempts to find out, from the Hubble Telescope to the International Space Station we are discovering hundreds of planets outside of our solar system that would have remained invisible mysteries to us here on Earth if we had never bothered to look. People used to think it complete foolishness to ever believe we would walk on the moon. All that we do know started with the pursuit of the once seemingly impossible.
I think that the main reason for this is that "unanswerable" questions do not remain unanswerable forever. At least, not all of them necessarily do. I would imagine that many things that we know now would have seemed like unanswerable questions to people not all that long ago.
For example, the idea that people could ever know what caused diseases would surely have seemed beyond belief to people a thousand years ago.
So, if science does not try to answer unanswerable questions, it might miss the chance to some discover new things.
It seems to me that human curiosity is one reason why Science seeks to answer that which is unanswerable. The use of data, generating hypotheses, and collaborating into a world of "the unknown" is what allows science to dare to dream of that which previously is unattainable or unanswerable. For example, think about the scientists who developed the first nuclear device. These were the best minds in the field brought to one area in order to solve a technical problem. They all knew of one another's reputation and the desire to collaborate, and to an extent, compete to solve the problem became the driving force. They were not fazed or deterred by the fact that the previous attempts had failed, or that they themselves might fail. There were not even stalled by the very real truth that their exploits were going to contribute to the immediate death of thousands and the changing of life for the negative as all knew it. In the final analysis, it was the desire to solve a problem, to cross a new intellectual frontier and "step across this line" that drove them.
The reason why science attempts to answer questions that most deem "unanswerable" is precisely because the purpose of the scientific method is to test variables.
A variable is a condition that is either dependent of its situation, or not dependent at all. Like, for example, if you sneeze in frontof pepper, the sneeze might or might not be dependant on the pepper, therefore, we experiment to establish a cause and an effect for things.
The task of science is to explore all elements around us. It is the process of scientific inquiry what has given a name to everything that has a name to this day. It is imperative that the scientific method and consistent exploration and experimentation of the world continue so that we, as members of a human race,and residents of Planet Earth finally get to understand this place where we live, and perhaps even the meaning of that little breathing timespan called "life".
The very definition of science is what makes it one of the few activities that can objectively and measurably answer questions that subjective activities such as philosophy can not. Science is the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. It represents activities restricted to a class of natural phenomena, and such activities applied to a definable or undefinable object of inquiry or study.
What is considered answerable today may be considered answerable future, and what is unanswerable today may be answered in future. This is the way progress in science takes place.
It is not possible for us to to know for certain whether a question is answerable or not. All that we can do is to ask a question and then try to find an answer for it. If answer for the question is known satisfactorily, there is no need for science to answer that same answer again.
Science has a role to play only when it encounters question for which no answer exists. There is no sure shot way to find out how easy or difficult it will be to find out the answer or whether or not a scientist will be able to find the answer in his or her life time. Scientist just strives to find the answers to questions that fancy them.
Mankind has a nature to know things. Our brains have developed for millions of years. It is because of this higher order intelligence that man has a need to make sense of the things around him.
Initially mankind began the scientific process as he tried to create implements that would help make life easier and solve dilemmas that they faced daily. Even now, the majority of scientific research is aimed at solving problems that exist in our world.
It is necessary for man to continue to search for answers. One reason is that as we develop new things, we create a new set of problems as well. There is always a cause and effect even for the best of discoveries. For example, antibiotics have saved millions of people's lives, but now mankind has developed resistance to many of the antibiotics that once worked to treat illness.
The unanswerable questions may be the most important ones for the world to know. Prior to many scientific discoveries mankind blamed events on supernatural occurances and in some cultures humans were used to sacrifice to the gods. Scientific discoveries both help prevent and initiate human rights protection as well as violations. As long as man exists there will always be the need to know more.