Build a vector
Set horizontal and vertical components, then connect them to magnitude and direction.
AP Physics 1 · Unit 1 · Kinematics
2D Vectors and Relative Motion
Build vectors from components, add them tip to tail, and steer a boat across a moving river using relative velocity.
Start lesson- Free
- No account required
- Self-paced
Start guided lesson
Learn by doing
Three ideas you’ll put into motion
Add two motions
Draw vectors tip to tail and compare their sum with component addition.
Choose a reference frame
Combine boat-through-water velocity with the current to predict the ground-relative trip.
The big idea
The key ideas, at a glance.
Components describe one vector
Perpendicular components combine as |v| = √(vx2 + vy2). Keep direction signs when adding.
Relative velocity adds vectors
The boat’s velocity relative to shore is its velocity through water plus the water’s velocity relative to shore.
A quick comparison
A boat heads across a river while the current flows downstream.
Shore motion = boat motion + current
Teaching this topic?Classroom fit, AP connections, and support
- Classroom fit
- Use for a concept introduction, guided independent practice, or a projected class discussion.
- Before students begin
- Signed coordinates, the Pythagorean theorem, and basic sine, cosine, and tangent.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 1: vector components, two-dimensional motion, and reference frames.
- Check for understanding
- Ask which velocity sets crossing time when the river current is parallel to the banks.
- Optional extension
- Practice vector addition with the Vector Displacement Scavenger Hunt.
Ready to test your thinking?
The first scene is set up. Start the lesson and explore.