Asia-Pacific Forum on Science Learning and Teaching, Volume 4, Issue 2, Article 8 (Dec., 2003) Tin-Lam TOH On using Geometer's Sketchpad to teach relative velocity Previous Contents Next

Example 1: Crossing the river

For most students learning Relative Velocity, one of the main difficulties is the resolution of vectors. Thus it is important to aid students in visualizing projection of vectors before plunging into the actual concepts of Relative Velocity. Here GSP can be useful to assist students in visualizing concept of projection of vectors.

One main setting of Relative Velocity is the scenario on "crossing the river". We shall assume that the banks of the river are two parallel lines, as shown in the Figure 1 below. The distance between the two parallel banks, as represented by the two parallel lines, is d unit. We shall further assume that the true speed of the boat is kept constant at v at an angle q to the bank

Figure 1

Then the time taken by the boat to cross the river

= =

.....(A)

By considering the projection along the direction marked by the distance d in Figure 1 above, another way to compute the time taken to cross the river

=

.....(B)

Both ways of computation, (A) and (B), give the same time for the boat to cross the river.
It may not be easy to convince Secondary school students that (A) and (B) give the same time, since the concept of "projection" is not in their Secondary School Science curriculum.

For a student who is not particularly well versed in trigonometry and geometry, GSP can be used to illustrate this clearly. The worksheet using GSP is introduced in Figure 2 below.

Figure 2: Worksheet for Example 1

In the above worksheet, the students click the button Animate Point on the screen to start the animation of the two points A and B. Initially both points A and B coincide with the point X. Upon clicking the Animate Point button, both points start to move from left to right as shown in the above diagram.

The point B represents the actual boat crossing the river while the point A is another particle that is dependent on the movement of B such that (i) AB is always parallel to the bank; and (ii) A and B reach the other shore at the same time.

The time taken by the boat B to cross the river can be calculated as , where the true distance refers to the actual distance traveled by the boat B. The time taken by the particle A, through the series of prompting questions in the worksheet (see Figure 2), can be computed as . Since both particles A and B reach the other shore at the same time, another way of computing the time taken to reach the other shore can be taken as . In many of the numerical questions in the typical examination questions, the use of to compute the time taken to cross the river may be much more straightforward.

 

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