## Friday, 16 October 2015

### Geometer's Sketchpad - Combining Velocity Vectors

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students will walk through a demonstration of how the combination of two linear motions can create a complex two dimensional motion (in this case circular motion). Some things that I think are important here are the fact that the two motions are completely independent of each other and the idea of how the look of a velocity vector changes as you speed up and slow down. The sketch is meant for students to walk through and answer questions as they go. You could also use it in the calculus part of the course to talk about velocity increasing/decreasing and what that looks like for motion.

• A1.1 - describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)
• C1.2 - represent a vector in two-space geometrically as a directed line segment, with direction expressed in different ways (e.g., 320º; N 40º W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors
• C2.1 - perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two space, and on vectors represented in Cartesian form in two-space and three-space