Linear Motion: Basic Vector Operations

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Adding Co-linear Vectors

AKA finding a resultant

Vectors are co-linear when their directions are parallel

Adding vectors that act in the same direction --> add magnitudes, use same direction

Adding vectors that act in opposite directions --> subtract magnitudes, use direction of larger vector

Adding Perpendicular Vectors

Use Basic Trigonometry:

Pythagoras' Theorem

Trigonometric functions: sine, cosine, tangent

Pythagoras' Theorem

The square of the hypotenuse is equal to the sum of the squares of the other two sides

Trigonometric Functions

Sine

Cosine

Tangent

Useful mnemonic: Silly Old Harry Caught A Herring Trawling Off America

Triangle Law for Perpendicular Vectors:

The resultant of any two perpendicular vectors is equal to the hypotenuse of the right-angled triangle formed by the two vectors placed "tip to tail"

The second vector starts at the end of the first vector

Use Pythagoras' Theorem to get the magnitude of the resultant vector

Use trigonometric functions to get the direction of the resultant vector

The diagram shows the addition of vectors AB and BC. The resultant vector is AC

Resolving Vectors

This is the opposite of finding the resultant

A vector is resolved into two component perpendicular vectors

The component vectors are equal to the magnitude of the original vector multiplied by sin θ and cos θ

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