Displacement on a Plane
Combine x and y displacements with vectors.
About this topic
In two dimensions, displacement is a vector with x and y parts. Add the components separately: a walk of 3 m east and 4 m north gives a displacement of 5 m at about 53° north of east, by the Pythagorean theorem and tangent.
Use Δx and Δy with trigonometry to resolve vectors. The magnitude is the square root of Δx² + Δy², and the angle comes from tan θ = Δy/Δx. The route taken doesn't change the displacement, only the start and end points do, whereas the distance depends on the entire path.
Example: a drone flies 30 m east, 40 m north, and then 10 m west. Total x displacement is 20 m east and y is 40 m north, so the displacement is about 44.7 m at about 63 degrees north of east, although it flew 80 m. Maps, GPS navigation, robotics and video games all rely on coordinate displacement.
Tips: draw a sketch and label directions clearly, and be careful with signs, taking west and south as negative. When finding an angle with the inverse tangent, check which quadrant your answer belongs in, since a calculator may give an angle in the wrong quadrant.
Key ideas
- Use components
- Magnitude via Pythagoras
- Direction via tan⁻¹(y/x)
Quick check
Use cases: where Displacement on a Plane helps
- Homework: review the key idea behind Displacement on a Plane before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Displacement on a Plane without notes.
- Visual learning: play with the interactive lab to see how Displacement on a Plane changes when you adjust its inputs.
- Teaching a friend: explain Displacement on a Plane in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Displacement on a Plane?
Combine x and y displacements with vectors.
What will I learn in Displacement on a Plane?
Use components. Magnitude via Pythagoras. Direction via tan⁻¹(y/x).
Is Displacement on a Plane part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Displacement on a Plane lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Displacement on a Plane?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.