Vectors and Projectiles Legacy Problem #1 Guided Solution

Two things are of importance in solving this problem correctly, and the first one is to have a solid understanding of the difference between distance and displacement, and to know the definitions of those two quantities. And the second thing is to have a pretty good understanding of what's going on in terms of the motion. So my mental picture of the motion is a coach walks north along the sideline, turns around and walks part of the way back southward towards the initial position, but never quite gets there. And I may ask two things, find the distance and find the displacement. Let's do distance first because that's probably the easiest one. When you're talking distance, you're talking how much ground is covered. You walk 26 yards to the north means you cover 26 yards, and you walk 12 yards to the south means you're covering another 12 yards. You've walked a total distance of 38 yards. And when you're considering distance, you pretty much ignore the direction. It's what I would call a direction unconscious quantity. On the other hand, displacement is a direction conscious quantity, and it takes into account whether an object is walking north or walking south. The simplest way to get at the displacement is to simply figure out where the person begins and where the person ends, and to find out how far it is from the beginning to the ending position. After all, displacement is how far out of place an object is from the beginning towards the end of the motion. So in this case, our coach starts 26 yards at a given position, walks north 26 yards, and back 12 yards, not quite to the beginning. At that point, the coach is 14 yards north of the starting point. And that's the displacement, 14 yards north.