A cyclist travels a distance of 1200m due north before going 200m due east followed by 500m south-west.Draw a scale diagram to calculate the cyclist's displacement from her initial position.
D = 1200m[90o] + 200[0o] + 500[225o].
X = 1200*Cos90 + 200*Cos0 + 500*Cos225 =
Y = 1200*sin90 + 200*sin0 + 500*sin225 =
Tan A = Y/X, A = ?.
D = X/Cos A, or Y/sin A.
To draw a scale diagram to calculate the cyclist's displacement, we first need to determine the scale of the diagram. Let's assume 1 cm on the diagram represents 100 meters in reality.
1. Start by drawing a horizontal line to represent the initial position of the cyclist. This line will represent the ground or the reference line.
2. Mark a point on this line to represent the cyclist's starting position (0m distance). Label it as 'A'.
3. From point 'A', draw a vertical line upwards of 12 cm (since 1 cm represents 100 m) to represent the cyclist's distance of 1200 m due north. Label the top point as 'B'.
4. From point 'B', draw a horizontal line of 2 cm to the right to represent the cyclist's 200 m move due east. Label the end point as 'C'.
5. From point 'C', draw a line downwards to the left of 5 cm (since 1 cm represents 100 m). This line represents the cyclist's 500 m move south-west. Label the end point as 'D'.
6. Finally, draw a straight line from point 'A' to point 'D'. This line represents the displacement of the cyclist from her initial position.
The length of this line can be measured using a ruler. To convert this measurement into actual displacement, we can use the scale: 1 cm = 100 m. Multiply the measured length in cm by 100 to get the displacement in meters.