A man walks 15m north then 20m at 32° E of N and then 11 m at at 15° S of W determine his net displacement
To determine the net displacement of the man, we need to find the resultant vector formed by adding the individual displacements.
Step 1: Convert the given distances and angles into rectangular (x, y) coordinates.
In the first displacement, the man walks 15m north. So, the x-component of the vector is 0 and the y-component is 15.
In the second displacement, the man walks 20m at 32°E of N. To find the x and y components, we can use trigonometry. The x-component can be calculated as 20 * sin(32°), which is approximately 10.66m. The y-component can be calculated as 20 * cos(32°), which is approximately 16.82m.
In the third displacement, the man walks 11m at 15°S of W. Again, using trigonometry, we can find the x and y components. The x-component is 11 * sin(15°), which is approximately 2.89m. The y-component is -11 * cos(15°), as it is in the negative y-direction, which is approximately -10.70m.
Step 2: Add up the x and y components of the three displacements.
Summing up the x-components: 0 + 10.66 + 2.89 = 13.55
Summing up the y-components: 15 + 16.82 - 10.70 = 21.12
Step 3: Calculate the magnitude and direction of the resultant vector.
To find the magnitude of the resultant vector, we can use the Pythagorean theorem:
Magnitude = √(x^2 + y^2) = √(13.55^2 + 21.12^2) = 25.11m (rounded to two decimal places)
To find the direction of the resultant vector, we can use trigonometry:
Direction = arctan(y/x) = arctan(21.12/13.55) = 56.17° (rounded to two decimal places)
Therefore, the man's net displacement is approximately 25.11m at an angle of 56.17° (measured counterclockwise from the positive x-axis).