Velocity composition

The purpose of this applet is to illustrate that velocity always is measured with respect to some reference frame and to illustrate the principle of velocity composition. This applet uses the example of a boat on a river.

In the case of a boay traveling on a river, there are three relevant velocities: the velocity of the boat with respect to the water, the velocity of the water with respect to the shore, and the velocity of the boat with respect to the shore. The velocity of the boat with respect to the water has a magnitude called the water speed and is in the same direction as the boat itself. The velocity of the boat with respect to the shore is calculated as the vector sum of the the other two velocities, using the following chain rule:

The user can adjust the following parameters:

• The water speed of the boat (using the slider on the left)
• The speed of the current (using the slider on the right)
• The direction in which the boat is pointing (by rotating the arrow on the lower left corner of the applet)

The user can also click and drag the boat on the screen. The motion can be frozen using the go/freeze button. If the boat hits the edge of the blue area, the motion is automatically frozen. To restart the applet, the user must turn the boat and/or adjust the velocities until the boat's velocity points away from the edge, or drag the boat away form the edge. The applet can then be restarted by clicking "go".

The velocity of the boat with respect to the water is drawn in pink, the velocity of the water with respect to the shore is drawn in grey, and the velocity of the boat with respect to the shore is drawn in black. Verify for yourself that the boat moves on the screen along the direction indicated by the black velocity vector.