Direction of Displacement Vector [2D Kinematics]

[stickyriceyum]

Homework Statement

Question 1 [Correctly Solved]
A pedestrian moves 2.1km east and then 20km north. Find the magnitude of the resultant displacement vector. Answer in units of km.

Answer = 20.1km

Question 2
What is the direction of the displacement vector (using the counter-clockwise angular direction to be positive, within the limits of -180 degrees = 180 degrees)? Answer in units of degrees/

The Attempt at a Solution

[Theta] = (arctan) (Ay/Ax)
[Theta] = (arctan) 20km/2.1km = 1.466

------

I'm probably using the wrong equation. :x
(using the counter-clockwise angular direction to be positive, within the limits of -180 degrees = 180 degrees) Also, I don't understand what that means. Will someone please explain?

 

[abelanger]

question #1: Draw it on a sheet of paper, make a Cartesian plane, use the upper y-axis as north, right x-axis as east. You ll remember something!
*hint* Pythagorean Theorem ;)

Question #2: now I am not sure if ill explain this right but! i think that this : "using the counter-clockwise angular direction to be positive, within the limits of -180 degrees = 180 degrees" means find the angle opposite to the 20km line (i think its the angle between the hypotenus and the 2.1km line)
Let's say it is ;)
now remember SOHCAHTOA and see if you can do it.

Got more questions, just PM me. Goodluck!

 

[baba89]

I would like to clarify that the direction of a displacement vector is usually measured in degrees or radians in a counterclockwise direction from the positive x-axis. In this case, the direction of the displacement vector would be 81.87 degrees, which can also be written as -98.13 degrees (since it is within the limits of -180 degrees to 180 degrees). This means that the pedestrian moved in a direction that is 81.87 degrees away from the positive x-axis, which would be in the northeast direction.

As for the calculation of the direction, the correct equation to use is [Theta] = tan^-1 (Dy/Dx), where Dy and Dx represent the change in y and x coordinates, respectively. In this case, Dy = 20km and Dx = 2.1km, which gives us [Theta] = tan^-1 (20km/2.1km) = 81.87 degrees.

I hope this clarifies any confusion and helps you understand the correct method for calculating the direction of a displacement vector.