A cyclist travels a distance of 1200m due north before going 2000m due east followed by 500m south-west. Draw a scale diagram to calculate the cyclist's final displacement form her initial position?
D = 1200m[90o] + 2000[0] + 500[225].
X = 1200*Cos90 + 2000*Cos0 + 500*Cos225 =
0 + 2000 - 354 = 1646 m.
Y = 1200*sin90 + 2000*sin0 + 500*sin225 =
1200 + 0 - 354 = 846 m.
Tan A = Y/X = 846/1646 = 0.51397.
A =
D = X/Cos A.
Oh boy, time to put my artistic skills to the test! Let me whip out my invisible paintbrush and create a masterpiece scale diagram for you.
Imagine you're looking down from the top (like a bird's eye view), and prepare to be amazed by my sketch.
First, draw a line pointing straight up to represent the cyclist's initial distance of 1200m due north. Label it "1200m."
Next, draw a line to the right at a right angle to represent the cyclist's 2000m due east. Label it "2000m."
Now, get ready for a little diagonal action. Draw a line pointing down and to the left to represent the cyclist's 500m southwest journey. Label it "500m SW."
Finally, I'll let you connect the ends of these three lines to form a triangle. Label the point where they intersect as "cyclist's final position."
Voila! You have your scale diagram depicting the cyclist's journey. Calculate the displacement by measuring the straight-line distance from the starting point to the ending point using a ruler, and there you have it!
To draw a scale diagram to calculate the cyclist's final displacement, we need to represent the distances and directions traveled on a coordinate plane.
Let's start by drawing a coordinate plane. We can use a piece of graph paper or draw our own. Label the x-axis for east/west and the y-axis for north/south.
Next, we'll plot the initial position of the cyclist. Suppose we start at the origin (0,0). This will be our starting point.
Next, the cyclist travels 1200m due north. We can draw a line segment going straight up from the origin for a distance of 1200 units on the y-axis.
Then, the cyclist goes 2000m due east. We can draw a line segment going to the right from the end of the previous line segment for a distance of 2000 units on the x-axis.
Finally, the cyclist goes 500m southwest. We can draw a line segment going down and to the left from the end of the previous line segment for a distance of 500 units on the y-axis and 500 units on the x-axis.
Now, to calculate the cyclist's final displacement, we can draw a straight line from the starting point to the endpoint of our diagram.
To determine the scale of our diagram, we need to decide on a ratio. For example, if 1 cm represents 100m, we can measure the distances traveled and draw the diagram accordingly.
Remember to label the distances on each line segment to keep track of the distances traveled.
To draw a scale diagram to calculate the cyclist's final displacement, we need to create a coordinate system and plot the distances traveled in each direction.
1. Start by drawing a straight line to represent the north direction and label it as "North."
2. Choose a suitable scale for your diagram. For example, you could use 1 cm to represent 100 meters.
3. Measure and mark a point 12 cm above the starting point to represent the 1200 meters traveled due north.
4. Draw another straight line to represent the east direction originating from the endpoint of the previous line and label it as "East."
5. Measure and mark a point 20 cm to the right from the endpoint of the previous line to represent the 2000 meters traveled due east.
6. Next, draw a line connecting the starting point and the endpoint of the previous line. This line should go diagonally towards the southwest.
7. Measure and mark a point 5 cm below and 5 cm to the left of the starting point to represent the 500 meters traveled southwest.
8. Finally, draw a straight line connecting the starting point and the endpoint of the previous line. This line represents the final displacement.
9. Calculate the length of the final displacement line (in cm) using a ruler.
10. Convert the length of the final displacement line from cm to meters by multiplying it by the scale you chose. For example, if your scale was 1 cm:100 meters, multiply the length in cm by 100.
11. Determine the direction of the final displacement line on the diagram (e.g., angle relative to north).
By following these steps, you can create a scale diagram to calculate the cyclist's final displacement from her initial position.