Find x and y component of vector a ?

Question

a) Find the x component of vector a (4.0m/s^2 , -y direction) 

 

b) Find the y compoent of vector a  (4.0m/s^2 , -y direction) 

 

What I dont understand is " -y direction" . On the cartesian plane, there are two -y directions , in the 3rd and fourth quadrant . Im so confused on how to work this out. 

Answer 1

To follow on David's answer, I think the confusion comes from mixing up a -y coordinate with the -y direction.  A -y coordinate is part of naming an individual point in either the third or fourth quadrants.  But the -y direction refers to a vector (often represented as an arrow) pointing in the direction where y gets more negative (which is, as David said, downward on a standard x-y plot).

 

The components of a vector represent, informally, "how much" of the vector points in (often) along horizontal (x) and vertical (y) lines.  By definition, this vector points only in the -y direction.  So how much of it is along a horizontal line?  This is the x component.  And how much of it is along a vertical line?  This is the y component. You will also have to note whether each component points in the + and - direction along that line.  [NOTE:  0 is a possible answer here].

 

Hope this helps some!  Just ask if you would like to talk more about it.

Answer 2

You are right in thinking that there are negative y values in the 3rd and 4th quadrants.  The negative y direction is downwards pointing on a cartesian plane if it were hung up on a wall, so it isn't tied to any one particular location on the cartesian plane, or quadrant for that matter.  You can think of the quadrants as more of fields or spaces than directions.

Let me know if that helps you sort this vector question out.  I'll give you a hint in that vertical lines have no horizontal components, and vice versa!  I'm pretty sure that you'll need to state the direction as well as the magnitude for a component of a vector, since they are still vectors.

Answer 3

Your question is confusing.  Vector a appears to have magnitude 4 meters/second² and every vector can be broken into two components, a horizontal vector & a vertical vector.  

 

We have to SEE the given vector (i.e. its direction angle θ) and then we COMPUTE component x = a(cos θ) and component y = a(sin θ).

 

The sign of the components comes out automatically, depending on θ.

 

If you known the angle, you can solve this problem.