HardPhysicsHigh School (11–12)Mechanics › Relative MotionMechanics › Vectors and Motion in a PlaneNumerical
A light aircraft flies at 240 km/h through the air.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A light aircraft flies at through the air. A steady wind blows towards the east at .
- The pilot points the plane due north. Find its speed over the ground, and its direction.
- Now the pilot wants to travel due north over the ground. In which direction must she point the plane, and what is her ground speed then?
Need a reminder? The key ideaShow
Velocity over the ground = velocity through the air + velocity of the wind. To keep a straight track, the pilot points the plane partly into the wind.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. East is and north is . Add the plane's velocity through the air and the wind.
Step 1. Pointing north. . Its size is , and its direction is east of north.
Step 2. Pointing into the wind. For a track due north, , so and west of north.
Step 3. Ground speed then. , due north.
Answer: (a) , at east of north. (b) Point the plane west of north; the ground speed is .
Check. In (b) part of the plane's speed is spent fighting the wind, so it goes slower than its air speed. In (a) the wind adds speed, but it pushes the plane off course.
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