|Asia-Pacific Forum on Science
Learning and Teaching, Volume 4, Issue 2, Article 8 (Dec., 2003)
On using Geometer's Sketchpad to teach relative velocity
Value added by using GSP
Consider Example 1: students could acquire a sound understanding of the concept of projection of a vector (in this case velocity vector) along a given direction (the direction that is perpendicular to the two parallel river banks) by visual impact, rather than by the traditional rote memory of equating the two expressions = (see Example 1). Resolution of vectors forms the foundation of Relative Velocity. To be confident in designing worksheets pertaining to this area, teachers need to be able to see this from the geometrical concept of similar figures and the related mechanics concept of resolving vectors.
Example 2 is another difficult concept for students to visualize: irregardless of the water speed of the boat, the boat must be steered perpendicular to the two parallel banks in order to reach the other shore in the shortest possible time. However, with the use of GSP, the following facts can be easily visualized by dragging the different directions of the boat: if the boat is steered upstream, it takes a longer time to reach the other shore since the true speed of the boat is reduced; if the boat is steered downstream, even though the speed of the boat is increased, it has to travel a much longer distance in order to reach the other shore. Thus, in order to reach the other shore in the shortest possible time, he must steer perpendicular to the two parallel banks.
Example 3 needs the physical interpretation of the subtraction of two vectors AB as 'treating' A as the origin. So, it is geometrically equivalent to translating the point A back to the same point at all time. The vector AB is the same in both systems. This was the relation of the Relative System and the Actual System. Thus, the concept of "Reduction to Rest" method of solving problems involving Relative Velocity can be given a more meaningful physical interpretation by using GSP.
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