I have a quick question about when we can define the initial velocity to be zero. For example, in projectile motion problems, even though we know that projectile is originally at rest in a cannon, we assign the initial velocity to be some number that we can work with. However, for problems involving the work-energy theorem, no matter whether the ball has some measurable velocity at the beginning, on earth, we say that the initial velocity is zero in order to conclude that the work done is opposite that of gravity. Therefore, it seems that we pick and choose to define when velocity is zero. Why can we say it's zero in one type of problem (like work-energy theorem problems) but not other problems (liek projectile motion problems)?