Applications of Vectors

Pre-Calculus · Axiom Academy

A plane points due east, but a crosswind has other plans. One idea — add the vectors — tells you exactly where it actually goes. Your plane flies 300 mph due east through air that is itself moving — a wind out of the north. Where you point and where you go are two different arrows. Three moves with one relationship sort it out. Add the arrows — where does it really go? The plane's velocity points east; the wind points south. Lay them tip-to-tail and a third arrow appears — the actual path over the ground. That third arrow is the resultant : velocity + wind. Break one arrow into east and north Adding arrows really means adding their pieces. So learn the one move it rests on: take a single 300 mph velocity aimed at some heading and split it into how much is east and how much is north — the legs of a right triangle. Steer into the wind — what does it cost? A pilot doesn't accept the drift — they aim into the wind so the sideways push cancels and the ground track runs true east. But canceling the wind spends part of the plane's speed sideways. Drag the wind and feel the tradeoff. One relationship, three moves: add the arrows to find the true result, break each arrow into components to actually compute it, and weigh the heading you choose against what it costs. The same three moves steer a boat across a current, balance forces on a hanging load, and resolve a satellite's thrust — anywhere two influences combine, add the vectors .

This is the written version of the interactive lesson above. See the full Pre-Calculus course.