Chapter 3

Two-Dimensional Motion and Vectors Pg. 82-112 Summary Pg. 112

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 added graphically Vectors can be moved parallel to themselves in a diagram Vectors can be added in any order To subtract a vector, add its opposite

Two dimensional Motion Vector operations uses the “x” and “y” axis. Last chapter This chapter

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

Determining resultant magnitude 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 direction To completely describe the resultant displacement you also need to find the direction When the displacement forms a right triangle, use the tangent function to find the angle (θ) of the displacement

Determining resultant direction The angle (θ) of the displacement is the direction of the displacement

Determining resultant direction To find just the angle, use the inverse of the tangent function

An archaeologist climbs the Great Pyramid in Giza, Egypt 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)