Two-Dimensional Motion and Vectors Pg Summary 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 symbols vectors in boldface scalars 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 are displacementvelocity accelerationforce momentumangular 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. Last chapterThis chapter

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

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 10 2 m, 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)