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In previous articles we covered the topic of resolving vectors, mainly the headings: how to resolve a vector, definitions and a complete guide on how to go about splitting/resolving a vector into its perpendicular components and how to label them, in this article we will look at some examples on how to resolve vectors.

To read more on resolving vectors click here

Question # 1

Calculate the horizontal and vertical components of a 50N force which is acting 40 degrees to the horizontal.

vector
Vector


Answer: 


The question asked for the values of the horizontal and vertical components, so first you need to split the vector seen in the diagram above into its horizontal and vertical components:


resolved vector
Resolved Vector


Now that you have identified both components the next thing that needs to be done is to label the components. Look at the diagram above and find out which of the components is adjacent to the given angle and label it “F×cosθ”, where F is the force and θ is the given angle. Also find out which component is opposite to the given angle and label it “F×sinθ”. In this example the component adjacent to the given angle is the horizontal component so it is labeled 50×cos 40 degrees. The component opposite to the given angle is the vertical component so it is labeled 50×sin40 degrees.


Resolved Vector
Resolved Vector



Therefore your answer should be:

Horizontal component = 50×cos40
                                  = 38.30N

Vertical Component = 50×sin40
                               = 32.14N
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Resolving vectors means splitting vectors into two perpendicular components.
Resolving vectors can be very easy if you’re focused. Here I’ll be showing you how to resolve a vector and then solve its horizontal and vertical components.

Using the vector below F it must first be split(resolved)  into its vertical and horizontal components before it can be solved.

Vector F

Vector when resolved



  1. Identify the component (line) adjacent to the given angle ‘A’(here it is the horizontal component).
  2.  Label the adjacent  component as F x COS A.

     3. Identify the component opposite to the given angle ‘A’(here it is the vertical component).
     4. Label opposite component as F x SIN A.




The following formulas can then be used to solve the components:

         Horizontal component = F x COS A
         Vertical component = F x SIN A

Note:  When resolving vectors the component adjacent to the given angle is ALWAYS the vector multiplied by the cosine(COS) of the angle while the component opposite the given angle is always the vector multiplied by the sin(SIN) of the angle.

Click here to see an example on how to resolve a vector
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Here is an example on how to solve a vector question:


Example #1:

A force of 3N acts at an angle of 90 degrees to a force of 4N. Find the magnitude and direction of there resultant R.

( Note: a line similar to the 3N was drawn on right to make the vector tail to head. The resultant line R was then drawn from the tail of 4N line to Head of 3N line on right. Also note that direction in this case is the unknown angle. )


Answer


Using Pythaoras' theorem to find magnitude.









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