1. Displacement

2. Defining Position  Position has three properties: Origin, magnitude, directionOrigin, magnitude, direction  1 dimension 12 feet above sea level.  Origin: sea level  Magnitude: 12 feet  Direction: up  2 dimensions 65 miles west of Chicago.  Origin: downtown Chicago  Magnitude: 65 miles  Direction: west  3 dimensions Range 200 m, bearing 270 , at 30  altitude.  Origin: observer  Magnitude: 200 meters  Direction: 270  by the compass and 30  up.

3. Position Graph  Position can be displayed on a graph. The origin for position is the origin on the graph.The origin for position is the origin on the graph. Axes are position coordinates.Axes are position coordinates. The position is a vector.The position is a vector.  A set of position points connected on a graph is a trajectory. y x 2-dimensions (x, y) position vector trajectory

4. Scalar Multiplication  A vector can be multiplied by a scalar. Change feet to meters.Change feet to meters. Walk twice as far in the same direction.Walk twice as far in the same direction.  Scalar multiplication multiplies each component by the same factor.  The result is a new vector, always parallel to the original vector.

5. Reference Point  Displacement is different from position Position is measured relative to an origin common to all points. Displacement is measured relative to the object’s initial position. The path (trajectory) doesn’t matter for displacement. trajectorydisplacement originposition

6. Displacement Vector  The position vector is often designated by.  A change in a quantity is designated by Δ (delta).  Always take the final value and subtract the initial value. y x

7. Two Displacements  A hiker starts at a point 2.0 km east of camp, then walks to a point 3.0 km northeast of camp. What is the displacement of the hiker?  Each individual displacement is a vector that can be represented by an arrow. 2.0 km 3.0 km

8. Vector Subtraction  To subtract two vectors, place both at the same origin.  Start at the tip of the first and go to the tip of the second.

9. Component Subtraction  Multiplying a vector by  1 will create an antiparallel vector of the same magnitude.  Vector subtraction is equivalent to scalar multiplication and addition.

10. Displacement Components  Find the components of each vector, and subtract. A x = 2.0 km A y = 0.0 km B x = (3.0 km)cos45 = 2.1 km B y = (3.0 km)sin45 = 2.1 km D x = B x – A x = 0.1 km D y = B y – A y = 2.1 km next