Resolving Vectors Questions & Answers Example 1

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.

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Question # 1

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

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

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

Therefore your answer should be:

Horizontal component = 50×cos40
                                  = 38.30N

Vertical Component = 50×sin40
                               = 32.14N