Chapter 3

Two-Dimensional Motion and Vectors

Pg. 82-112Summary Pg. 112

• Imagine that you have a map that

leads you to a buried treasure.

• This map has instructions such as

15 paces to the north

of the skull.

• The 15 paces is

a distance and

north is a direction.

N

Scalar – a quantity that has a magnitude (number), but no direction

ex. Volume, mass 3 kg

Vector - a quantity that has a magnitude (number) and direction

ex. velocity, displacement, acceleration

3 m/s south

Vectors are represented by symbolsvectors in

boldfacescalars in

italics

Vectors can be added graphically

• Resultant – answer found by adding vectors

• Vectors can be moved parallel to themselves in a diagram

• Vectors can be added in any order

• To subtract a vector, add its opposite

Vectors can be added graphically

• Vectors: physical quantity with both magnitude and direction

• Examples of vectors in physics aredisplacement velocityacceleration forcemomentum angular momentum

• Keep track of vectors using symbols and diagrams–Example:

• If 2 more vectors act on the same point it is possible to find a resultant vector that has the same effect as the combo of individual vectors.

• The walkway will take the car and move it side ways before it drives off. The resultant velocity will be at an angle.–Vectors can be moved parallel to

themselves in a diagram–Vectors can be added in any order–To subtract a vector, add its opposite–Multiplying/dividing vectors by scalars

result in vectors.

Two dimensional Motion

• Vector operations uses the “x” and “y” axis.

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Determining resultant magnitude

• If the movement is a straight line, Use the Pythagorean theorem to find the magnitude of the resultant

• Pythagorean Theorem for right triangles

d2 = x2 + y2

(Length of hypotenuse)2 = (length of one leg)2 + (length of the other leg)2

Determining resultant magnitude

Determining resultant magnitude

• To completely describe the resultant you also need to find the direction also

• When the resultant forms a right triangle, use the tangent function to find the angle (θ) of the resultant

Determining resultant direction

• The angle (θ) of the resultant is the direction of the resultant

Determining resultant direction

Determining resultant direction

To find just the angle, use the inverse of the tangent function

An archaeologist climbs the Great Pyramid in Giza, Egypt. If the pyramid’s height is 136 m and its width is 2.30 x 102m, what is the magnitude and the direction of the archaeologist’s displacement while climbing from the bottom of the pyramid to the top?

• Remember when you solve for the displacement you are looking for the magnitude (d) and the direction (Θ)