During athletics day at school, a learner broke a record by running 800 m in 1 minute and 49 seconds. He ran the 800 m in the following manner: first, he ran 300 m west and then 500 m southwest.

Construct a vector-scale diagram to represent the displacement of the learner in meters.

(Use the scale 1 cm = 100 m.)

To represent the learner's displacement, a vector-scale diagram can be constructed with an arrow of 8 cm in the west direction and 5 cm in the south direction. The total displacement is (-800 m, -500 m).

Explanation:

To construct a vector-scale diagram representing the displacement of the learner, we first need to determine the total displacement. The learner ran 300 m west, which is a displacement of -300 m in the x-direction. Then, the learner ran 500 m southwest, which can be broken down into two components: 500 m in the south direction and 500 m in the west direction. The south component is -500 m and the west component is -500 m.

To find the total displacement, we sum up the x-component and y-component of the displacement. In this case, the x-component is -300 m + (-500 m) = -800 m and the y-component is -500 m. Therefore, the total displacement is (-800 m, -500 m) on the vector-scale diagram.

Using the given scale of 1 cm = 100 m, we can represent the displacement on the vector-scale diagram by drawing an arrow with a length of 8 cm in the west direction and 5 cm in the south direction.

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