I know how to do displacement, I just get confused by the directions. I walk 6 blocks east and 5 blocks north-I come up with 7.8 because I squared 6 + squared 5 and took the square root of 61 but do I say the final displacement is 7.8 blocks east of north or 7.8 blocks north of east-that's where I'm confused.
Thank you
Try it with x and y
x is east and y is north
start at (0,0)
go east 6 to (6,0)
now go north 5 to (6,5)
now what angle north of east is (6,5)?
tan angle = y/x = 5/6 so angle = 39.8 deg
usually you want compass directions clockwise from north though so
90 = 39.8 = 50.2 degrees east of north
now I better check your distance
sqrt(36+25) = sqrt 61 = 7.8 check
so
you went 7.8 blocks at 50.2 degrees east of north
When determining the direction of the displacement, it's important to use the convention of specifying the direction as an angle measured from a reference direction, which is usually the positive x-axis (east) in a Cartesian coordinate system.
In your case, you walked 6 blocks east and 5 blocks north, resulting in a displacement of 7.8 blocks. To determine the direction, you need to find the angle between the displacement vector and the positive x-axis.
To do this, you can use trigonometry. The angle, θ, can be found using the inverse tangent function:
θ = arctan(y / x)
where y is the distance north and x is the distance east.
Plugging in the values, you get:
θ = arctan(5 / 6)
Using a calculator, this gives you an angle of approximately 40.56 degrees.
Now, to specify the final direction, you would say "7.8 blocks at an angle of 40.56 degrees east of north." The "east of north" part indicates that the displacement is measured from the north direction, with a positive angle indicating a direction counterclockwise from the reference direction.
So, to answer your question, the final displacement is 7.8 blocks east of north.