Question

A Jogger runs 2.0km due east, then 10km at 45° north of east and finally 0.5km due north- Determine the displacement using graphical method Using Scale of 5ocm =2 km​

Answer 1

Using a graphical method and a scale of 5 cm = 2 km, the displacement of the jogger can be determined by drawing a vector diagram with a horizontal line for east and subsequent vectors for each leg of the journey. The resultant vector's length provides the jogger's total displacement, and the angle gives the direction north of east.

Step-by-step explanation:

To determine the displacement of the jogger using a graphical method with the stipulated scale of 5 cm = 2 km, we will construct a vector diagram to represent the jogger's movements.

Steps to Calculate Displacement:

1. Draw a horizontal line to represent east direction.
2. From the start point, draw a 2.0 km eastward vector (5 cm).
3. From the end of the first vector, draw a 10 km vector at a 45° angle north of east (25 cm at 45°).
4. From the end of the second vector, draw a 0.5 km vector northward (1.25 cm).
5. Using a ruler and protractor, accurately draw these vectors to scale and angle.
6. The resultant displacement is a vector from the start point directly to the end of the final vector.
7. Measure the length of the resultant vector and use the scale to convert this back to kilometers.
8. Determine the angle of the resultant vector using a protractor, which gives the direction north of east.

The length of the displacement vector will represent the jogger's total displacement in km, and the angle indicates the direction relative to due east. Make sure to adjust the measurements according to the given scale.