The example treated here is based on Exercise 5 from the Activities under Related Items in the bottom left corner. Have a look at this Exercise before you continue.

Exercise 5 deals with a ball that is being moved from a point A to a point B along three successive straight-line path segments. The diagram below illustrates the situation. It shows the path taken by the ball in blue and the displacement vector of the ball in green. The scalar components d_x and d_y of the displacement are shown in green as well.

The diagram is based on the applet on Page 2. For instructions on how to use the applet go to Applet Help on the applet's Help menu.

The distance traveled by the ball, s, is the length of the blue path taken by the ball. The value of s is obtained as follows.

The path consists of three straight-line segments:

• 5 m downward,
• 35 m to the left,
• 35 m upward.

Thus,

s = 5 + 35 + 35 = 75 m.

The distance traveled by the ball must be distinguished from the (straight-line) distance between the ball's initial and final positions A and B. The latter is equal to the magnitude d of the ball's displacement . What is the value of d in this case?

The components d_x and d_y of and the vector form a right-angle triangle, with as the hypotenuse. Therefore, the magnitude d of is given by the Pythagorean theorem,

Note that d < s. The straight-line distance between two points is the shortest connection between the points.