How do you use component vectors to solve real-world and applied problems?
Often when two processes interact we only know the component vector values and need to be able to combine these to get a desired result.
This might be more easily understood by an example:
Suppose I am trying to fly from point A to point B which is due North of point A. My plane flies at an air speed of 100 miles/hour but there is a wind blowing due West at 30 miles/hour. How many degrees East of North do I need to orient my plane to fly in a straight line to B?
From the above diagram, I need to head my plane (approximately)
This problem could be extended to ask:
If it is 200 miles from A to B and my plane has enough gas to fly 250 miles will I be able to make this trip?