The end of this journey is actually visible from the start. The distance traveled is a reasonable 14 km, but the resultant displacement is a mere 2.7 km north. Reverse direction and head downriver for 4.5 km.Cross using the George Washington Bridge (1.8 km between anchorages).Follow the Hudson River 8.2 km upriver.Your humble author occasionally rides his bicycle from Manhattan to New Jersey in search of discount そば ( soba) and さけ ( sake) at a large Japanese grocery store on the other side of the Hudson River. At the end of a year's time the Earth is right back where it started from. How far does the Earth travel in one year? In terms of distance, quite far (the circumference of the Earth's orbit is nearly one trillion meters), but in terms of displacement, not far at all (in some respects, zero). Displacement is a vector measure of the interval between two locations measured along the shortest path connecting them. Distance is a scalar measure of the interval between two locations measured along the actual path connecting them. Let's clarify by defining each of these words more precisely. The question is ambiguous and depends on whether the questioner meant to ask for the distance or displacement. On the other hand, the end point of my walk is two meters to the south of my starting point. On the one hand, there's the sum of the smaller motions that I made: two meters east, two meters south, two meters west resulting in a total walk of six meters. There are two ways to answer this question. Every year in class, I do the same moronic demonstration where I start at one side of the lecture table and walk to the other side and then ask "How far have I gone?" Look at the diagram below and then answer the question. That being said, let me deconstruct the definition of distance I just gave you. In casual conversation, it's often all right to state distances this way, but in most of physics this is unacceptable. What's being described in these examples is not distance, but time. They're all ninety minutes, but nobody would say they were all the same distance. The odd thing is that sometimes we state distances as times. (This is not the final definition.) The "distance" is the answer to the question, "How far is it from this to that or between this and that?" How far is it? how far is it Distance is a measure of the interval between two locations. Nevertheless I've come up with a preliminary definition that I think is rather good. ![]() ![]() It's one of those innate concepts that doesn't seem to require explanation. I've got to assume that everybody reading this has an idea of what distance is.
0 Comments
Leave a Reply. |