A vector is an object that has both a magnitude and direction. Examples include displacement, velocity, and force. Any vector in a plane can be decomposed into two perpendicular components.
Example: In the Jules Verne novel Mysterious Island, Captain Cyrus
Harding wants to find the height of a cliff. He stands with this back to the
base of the cliff, then marches straight back from it for 500 ft. He then lies
down on the ground and measures the angle from the horizontal to the top of the
cliff. If the angle is 30º, how tall is the cliff?
Solution:
Example: A jogger runs 145 m in a direction 20.0° east of north
(displacement vector A) and then 105 m in a direction 35.0° south of east
(displacement vector B). What is the jogger’s net displacement?
Solution: A good start is a sketch of the two vectors and their resultant.
Each component of the resultant is equal to the algebraic sum of the two
vectors, A and B.
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