How to resolve vectors easily?

If we take a single vector we can find a pair of vectors at right angles to each other that would combine to give the single original vector. This reverse process is called resolution or resolving vectors. The pair of vectors are called the resolved vectors.

The resolved pair of vectors will both start at the same point as the original single vector. And as said earlier, the angle between the resolved vectors is 90 degrees and if these two resolved vectors are added following the vector addition rules then the resultant vector will be the original vector we started off with.

Steps to resolve a vector with calculations

In order to resolve a vector into a pair at right angles, we must know its size (denoting the magnitude of the vector quantity) and direction.

The direction is most commonly given as an angle to either the vertical or the horizontal. This is useful as we most commonly want to split the vector up into a horizontal and vertical pair.

Let’s take an example of a Velocity Vector which has a magnitude of 4.2 m/s and its direction makes an angle of 40 degrees with the vertical, as shown in the figure below.

Resolving a velocity vector
figure 1: Resolving a velocity vector

Resolving a vector Step 1 – Getting the vertical component

Redrawing components from figure 1 to show how they add up to produce the velocity vector 4.2 m/s, we get figure 2. Here we see the components making a right angled triangle.

Redrawing the components to use trigonometry
figure 2: Redrawing the components

Using Trigonometry, we can say that:

cos 40 = Vy/4.2
=> Vy = 4.2 cos 40 = 4.2 x 0.766 = 3.2 m/s

Resolving a vector Step 2 – Getting the horizontal component

similarly,
Sin 40 = Vx/4.2
=> Vx = 4.2 sin 40 = 4.2 x 0.643 = 2.7 m/s

Summary:

Thus we can resolve a vector into 2 components, (1) Vertical & (2) Horizontal. Resolving a vector is an important step to solve physics numerical involving vector quantities.


Reference / Similar topics:

Vector Addition

Vector Subtraction

How to resolve vectors easily?
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