Question

A journey consists of two displacements: the first is 500m in a northerly direction and the second is 200m in an easterly direction. In a space below draw, to scale, a vector diagram of these displacements. State the scale of your diagram. On your diagram, show the two displacements and the resultant displacement. Determine the size (magnitude) and direction of the resultant displacement.

Answer 1

To draw a vector diagram of the two displacements, first determine the scale of the diagram. Then, draw line segments representing the displacements and the resultant displacement. Finally, use the Pythagorean theorem and trigonometry to determine the magnitude and direction of the resultant displacement.

Step-by-step explanation:

To draw a vector diagram of the two displacements, we need to determine the scale. Let's say 1 cm on the diagram represents 100 m.

First, draw a line segment pointing north that is 5 cm long to represent the 500 m northward displacement. Then, draw a line segment pointing east that is 2 cm long to represent the 200 m eastward displacement. Finally, draw a line segment from the starting point to the end point of the two displacements, which represents the resultant displacement.

To determine the magnitude and direction of the resultant displacement, we can use the Pythagorean theorem and trigonometry. The magnitude can be found using the formula sqrt((500)^2 + (200)^2), which is approximately 538 m. The direction can be found using the formula tan^(-1)((200)/(500)), which is approximately 21.8 degrees north of east.