Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Velocity and force as vectors
Resolve and combine velocity or force quantities with vectors
Problem types
- Resultants of velocities and forces
Builds on
- Vectors and their components
- A system written as a matrix equation · Useful idea
Finding components of vectors that add to a given resultant solves a linear system.
- Motion described by a parameter · Useful idea
A position (x(t), y(t)) is a vector that changes at a constant velocity vector (a, b), whose length is the speed.
Leads to
- The laws of sines and cosines · See it applied
Two forces or velocities that are not perpendicular form a triangle with their resultant, so the law of cosines gives the resultant's magnitude and the law of sines its direction.
Related skills
- The complex plane · Related idea
Adding force or velocity vectors is the same as adding complex numbers as points in the plane.
- Operations on matrices · Related idea
A vector is written as a column matrix, and matrices act on vectors by multiplication.
- Choosing a periodic model · Related idea
The position of a point moving around a circle is a vector whose components are a cosine and a sine of time.
- When given measures make a triangle · Related idea
Two vectors and their sum form a triangle, so the length of the sum must obey the triangle inequality.
- Matrices as transformations of the plane · Shared foundations
Open the interactive map to explore lessons and skill connections.