A newspaper carrier on delivery route travels 200.-m South-West and 300.-m West. What is the direction of the displacement

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To find the direction of the displacement, we need to determine the angle between the displacement vector and the reference direction, typically the positive x-axis.

Let's break down the given distance traveled:
- 200 m South-West: This can be divided into two components, 200 m south and 200 m west.
- 300 m West

Now, let's calculate the resultant displacement:

To find the resultant displacement in the horizontal direction (west), we can simply sum up the horizontal components of the distances traveled:
200 m West + 300 m West = 500 m West

To find the resultant displacement in the vertical direction (south), we can sum up the vertical components of the distances traveled:
200 m South

So, the displacement can be represented as a vector: (500 m West, 200 m South)

To find the angle between this displacement vector and the positive x-axis (east), we can use the trigonometric tangent function:
tan(angle) = (vertical component / horizontal component)
tan(angle) = (200 m / 500 m)

To calculate the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(200 m / 500 m)

Using a calculator or a trigonometric table, we can find the angle to be approximately 21.8 degrees.

Therefore, the direction of the displacement is 21.8 degrees south of west.