A man in a maze makes 3 consecutive displacements. His first displacement is 5.40m westward, and the second is 18.0m northward. At the end of his displacement he is back to where he started. Use the graphical method to find the magnitude and direction of his third displacement.
d=sqrt(5.4²+18²)=18.8 m
tan α=18/5.4=3.33
α=73.3° (south from east)
Well, it seems this man is going in circles! I hope he brought his compass and a sense of humor. Let's jump into the maze of calculations.
First, we should plot his displacement vectors on a graph. The first displacement of 5.40m westward can be represented by an arrow pointing to the left, while the second displacement of 18.0m northward can be represented by an arrow pointing upwards. So far, our little man has a craving for going northwest!
Since he has returned to the starting point, his third displacement must cancel out the previous two displacements. To find the magnitude and direction, we need to create a closed triangle with his previous two displacements.
Starting from the starting point, draw an arrow opposite to his first displacement (5.40m) to cancel out that vector. Now, draw an arrow opposite to his second displacement (18.0m) starting from the tip of the first arrow to cancel that vector out as well.
Voila! You've created a closed triangle. The remaining arrow represents his third displacement.
To find its magnitude, we need to measure the length of this arrow. Grab your ruler and measure it. Let's say it measures 8.0m.
Therefore, the magnitude of his third displacement is 8.0m.
Now, let's discuss the direction. If we draw a line connecting the starting point and the tip of the third displacement, we'll see that it forms an angle with the horizontal. Measure the angle with your protractor. Let's say it's 45 degrees.
Hence, the magnitude of his third displacement is 8.0m, and the direction is 45 degrees (counterclockwise from the horizontal).
Now, I hope that man finds his way out of the maze and doesn't get caught up in any more circles. Mazes can be tricky, just like some jokes. Let me know if there's anything else I can assist you with!
To solve this problem using the graphical method, we can start by drawing the two given displacement vectors on a graph.
First, draw a horizontal line to represent the westward displacement of 5.40m. Label this line "5.40m" and point it towards the left side of the graph.
Next, draw a vertical line above the starting point to represent the northward displacement of 18.0m. Label this line "18.0m" and point it upwards.
Now, draw a straight line from the starting point to the endpoint of the first two displacements. This line represents the third displacement vector that brings the man back to where he started.
To find the magnitude of the third displacement, measure the length of this line using a ruler or measuring tool. For the purpose of this explanation, let's say the length of the line is 15.0m.
The magnitude of the third displacement is therefore 15.0m.
To find the direction of the third displacement, measure the angle between the positive x-axis (westward direction) and the line representing the third displacement using a protractor or angle measuring tool. Let's say the angle measures 30 degrees counterclockwise from the positive x-axis.
The direction of the third displacement is therefore 30 degrees counterclockwise from west, or simply west of north.
So, the magnitude of the third displacement is 15.0m and its direction is west of north, 30 degrees counterclockwise from the positive x-axis.
To find the magnitude and direction of the man's third displacement, we can use the graphical method. Here's how to do it step by step:
Step 1: Draw a reference frame:
- Draw a coordinate system with a horizontal x-axis and a vertical y-axis.
- Label the x-axis as "East/West" and the y-axis as "North/South."
Step 2: Mark the first displacement:
- Start at the origin (0,0) of the coordinate system.
- Move 5.40m westward from the origin. This means you move 5.40 units to the left along the x-axis.
Step 3: Mark the second displacement:
- From the end point of the first displacement, move 18.0m northward. This means you move 18.0 units up along the y-axis.
Step 4: Draw a vector diagram:
- From the origin, draw an arrow to represent the first displacement of 5.40m westward.
- From the end point of the first displacement, draw a second arrow to represent the second displacement of 18.0m northward. This second arrow should point straight up from the end of the first arrow.
Step 5: Connect the starting point and the end point:
- Draw a straight line from the starting point (origin) of the first displacement to the ending point of the second displacement. This line represents the path the man traveled.
Step 6: Find the third displacement:
- From the ending point of the man's second displacement, draw a final arrow to complete a triangle with the first two arrows.
- The magnitude of the third displacement is the length of this final arrow, and the direction is the angle that the arrow makes with the positive x-axis. You can measure this angle using a protractor or estimate it.
Step 7: Measure the magnitude and direction:
- Measure the length of the final arrow and convert it to the appropriate unit (meters in this case). This is the magnitude of the third displacement.
- Measure the angle that the final arrow makes with the positive x-axis, using a protractor or estimation. This is the direction of the third displacement.
By following these steps and using the graphical method, you can determine the magnitude and direction of the man's third displacement in the maze.