In order for an action to be a sin there must be three things present;the act is bad.the intent was to commit the act - intend to do a bad thing.the will is free in it's consent to commit the act - freely choose to do it.While the presence of any of the three can be a matter of degree, that goes only to the gravity of the sin and the degree to which the individual can be held accountable for it.No question that killing someone is bad, it is not a good thing. The baby in this scenario is about to die, no matter what is done (assuming the bomb is real). But whether killed by my hand or the bomb, the act of taking that life is bad.My intention in committing the bad act - kill the baby - is to save many people and consequently myself as well (yet I volunteered in this situation so we can forego considering any selfish desire). My intent in committing this bad act is therefore noble, a good thing, though it does not lesson the repulsion of what must be done; ie a bad thing.There is no indication in the given scenario that my will is not free to consent - am not being forced to volunteer for this mission. However, something could be said for being put in a position of causing the death of one to save many or even just oneself (though not the later case here). A person in such a position could be seen as being forced to do something that otherwise goes against their will. So the will in this scenario could be seen as not entirely free.Being accountable addresses whether or not an act, if bad, could be justified. Being justified in a bad action, here killing a baby, does not change that act from bad to good. It just means it is not a sin. It is not a sin because the second and third things required to make this act a sin are not met.As to murder being "acceptable", that depends on one's definition of murder. Also think "justified" is a better choice of words than acceptable. Normally for killing someone to be called "murder" the presence of both intent and full consent of the will are implied by the word.Euthanasia, often called mercy killing, is another topic. In the broader sense which people often use this word, the acts in question are bad, the intent is wrong and the will is fully consenting to the act. Some might say it is perhaps a matter of definition. Think it is a bad thing and a sin when we decided to take action, with the intent and consent to kill somebody. When I say a sin, am not speaking here of the decision to withdraw extra-ordinary means of keeping a body breathing or heart beating. Would not call that decision a matter of euthanasia myself or to relieve people from the pain of great suffering. In the latter case we are not speaking of fatal overdose so that death relieves the suffering. A doctor knows that a course of pain relief will often lead to other complications including probable death (IOW death but not from OD), but the decision is made to administer the meds for pain anyway to ease suffering. These are all very personal choices, and things that can be freely expressed and consented to by the ill before getting to the point where they are unable to express it themselves. I do not call such decisions euthanasia myself. People that wish to lump these actions into the idea of euthanasia;that it should be ok to kill anyone wanting to die or who is deemed by someone else to be "better off" dead; are only looking for justification by appealing to our sense of mercy. To me these are not the same issues.