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.
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To draw a vector diagram of the two displacements, follow these steps:
1. Draw a straight line to represent the initial position, and label it as "Start."
2. From the endpoint of the initial position, draw a vertical line upward to represent the first displacement of 500m in a northerly direction. Label it as "Displacement 1."
3. From the endpoint of the first displacement, draw a horizontal line to the right to represent the second displacement of 200m in an easterly direction. Label it as "Displacement 2."
4. Use a ruler or scale to ensure that the lengths of the lines accurately reflect the magnitudes. For example, you can assign a scale of 1 cm = 100m, which means each centimeter on the diagram represents 100 meters in real life.
5. Finally, draw a straight line from the starting point to the endpoint of the second displacement to represent the resultant displacement. Label it as "Resultant Displacement."
To determine the magnitude and direction of the resultant displacement, you can use the Pythagorean theorem and trigonometric functions. Here's how:
1. Use the Pythagorean theorem to find the magnitude (size) of the resultant displacement. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the resultant displacement, and the other two sides are the two displacements.
- magnitude of the resultant displacement = √(500² + 200²) = √(250000 + 40000) = √290000 = 539.58m (rounded to two decimal places)
2. Use trigonometric functions to find the direction of the resultant displacement. In this case, you can use the inverse tangent function (tan⁻¹) to find the angle.
- angle = tan⁻¹(500 / 200) = tan⁻¹(2.5) = 67.38° (rounded to two decimal places)
- Note: Make sure to correctly assign the angle based on the quadrants of the coordinate plane.
Now, you have the magnitude of the resultant displacement (539.58m) and the direction (67.38°). You can label this information on your vector diagram to complete the answer.