For instance, if the wind velocity increased, then the plane would still be covering ground in the northerly direction at the same rate. An alteration in one of the components will not affect the other component. These two components are independent of each other.
The northwest velocity vector consists of two components - a north component resulting from the plane's motor (the plane velocity) and a westward component resulting from the crosswind (the wind velocity). If the plane encounters a crosswind directed towards the west, then the resulting velocity of the plane would be northwest. Suppose that a plane is attempting to fly northward from Chicago to the Canada border by simply directing the plane due northward. The resulting motion of a plane flying in the presence of a crosswind is the combination (or sum) of two simultaneous velocity vectors that are perpendicular to each other. While the change in one of the components will alter the magnitude of the resulting force, it does not alter the magnitude of the other component. Changing a component will affect the motion in that specific direction. This is what is meant by the phrase "perpendicular components of vectors are independent of each other." A change in one component does not affect the other component. A change in the horizontal component does not affect the vertical component.
Pulling horizontally with more force does not lift Fido vertically off the ground. If the horizontal pull upon Fido increases, then Fido would be accelerated at a greater rate to the right yet this greater horizontal pull would not exert any vertical influence upon Fido. Consider the pull upon Fido as an example. The two perpendicular parts or components of a vector are independent of each other. These two components can be represented as legs of a right triangle formed by projecting the vector onto the x- and y-axis. directed at an angle can be thought of as being composed of two perpendicular components. This is depicted in the diagram below.Īny vector - whether it is a force vector, displacement vector, velocity vector, etc. The vector sum of these two components is always equal to the force at the given angle. Any force vector that is exerted at an angle to the horizontal can be considered as having two parts or components. A component describes the effect of a single vector in a given direction. These two parts of the two-dimensional vector are referred to as components. That is to say, if you pull upon an object in an upward and rightward direction, then you are exerting an influence upon the object in two separate directions - an upward direction and a rightward direction. A force vector that is directed upward and rightward has two parts - an upward part and a rightward part.
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