Free Fall: Vectors

Introduction to Vectors:

"The pendulum of the mind alternates between sense and nonsense, not between right and wrong."

A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude. Although a vector has magnitude and direction, it does not have a position. That is, as long as it's length is not changed, a vector is not altered if it is displaced parallel to itself.

Applications on Everyday Life:

Aircraft in flight are subject to the direction of the winds in which the aircraft is operating. For example, an aircraft in flight that is pointed directly north along its longitudinal axis will, generally, fly in that northerly direction. However, if there is a west wind in the air in which the aircraft is flying, then the actual trajectory of the aircraft will be slightly to the east of north. If the aircraft was landing on a northbound runway, it would need to compensate for this easterly component of velocity caused by the west crosswind.

We experience and interpret vectors in our everyday lives whether through photos, diagrams, architecture, or advertisements. Vectors tell us visually what we would normally say verbally.

Vector Operations:

Graphical Vector Addition

Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point. The process can be done mathematically by finding the components of A and B,combining to form the components of R.

Components of a Vector:

Finding the components of vectors for vector addition involves forming a right triangle from each vector and using the standard triangle trigonometry.

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