You walk 80 m to the north, then turn 60 degrees to your right and walk another 45 m. Determine the direction of your displacement vector. Express answer relative to east :)
Wouldn't you take tan-1 of Y/X
Y= 80 because you're heading north on a y-axis then 45 m would be your x-axis so tan-1 (80/45)??
50,82
To determine the direction of your displacement vector, we need to break it down into its north and east components.
First, let's find the north component of your displacement. Walking 80 m to the north means you have moved 80 m in the positive north direction.
Next, we need to find the east component. Turning 60 degrees to your right is the same as turning 30 degrees to your north-east (since 90 degrees is east, and 60 degrees is south-east). So, you have walked 45 m in this north-east direction.
To get the total displacement, we need to add the north and east components together. Since the north component is already positive, and the east component is in the positive north-east direction, we can simply express the answer as:
80 m north + 45 m north-east
Simplifying this, we have:
80 m + 45 m north-east
Finally, we can convert the north-east direction into its east component. Since the north-east direction forms a 45-45-90 triangle, we know that the east component is equal to the north component. Therefore, we can express the answer as:
80 m + 45 m east
So, the direction of your displacement vector is 80 m + 45 m east.