Chapter 3 Review of properties of vectors A vector is a quantity with Magnitude and Direction

Figure 3-2 A Walk Along City Streets to the Library

Figure 3-4 A Vector and Its Scalar Components

Example 3-1 Determining the Height of a Cliff

Figure 3-5 A Vector Whose x and y Components Are Positive

Figure 3-6ab Examples of Vectors with Components of Different Signs

Figure 3-6cd Examples of Vectors with Components of Different Signs

Most often, the angle to the “x” axis will be given. Figure 3-7 Vector Angle Most often, the angle to the “x” axis will be given.

Figure 3-8 The Sum of Two Vectors

Physlet Exploration 3.5 addition of vectors

Figure 3-9 Adding Several Vectors

Figure 3-10 Identical Vectors A at Different Locations

NOTE: A vector does not have a specific “origin” in space. Figure 3-11 A + B = B + A NOTE: A vector does not have a specific “origin” in space.

Figure 3-13a Component Addition of Vectors

Figure 3-14 Vector Subtraction

Figure 3-15 Unit Vectors

Figure 3-19 Displacement Vector

Figure 3-20 Average Velocity Vector Note: 2D NOW! Velocity is parallel to displacement.

Figure 3-23 Average Acceleration for a Car Traveling in a Circle With Constant Speed Note how we can move the final velocity vector to solve the problem—a vector does not have a specific location in space. This problem is easy, if we use the definition of average acceleration.

Figure 3-22 Average Acceleration Vector Note: position-position graph, 2D. NOT x vs. t

How do we know what direction the acceleration points? Figure 3-24 Velocity and Acceleration Vectors for a Particle Moving Along a Winding Path How do we know what direction the acceleration points? Note: this is a “distance-distance” graph, not distance-time.

Figure 3-25 Relative Velocity of a Passenger on a Train with Respect to a Person on the Ground

Figure 3-27 Relative Velocity in Two Dimensions

Example 3-2 Crossing a River Vheading Vwater Vtrack Navigation Problem: Given desired track and speed of water, what heading should you take?

Figure 3-30 Conceptual Question 3-2 Which of these vectors are equal?

Which 2 vectors are equal? H,K and F,I G,J and I,L NONE ARE EQUAL Cross-Tab Label 0 / 100

Figure 3-36 Problems 3-28 and 3-29

Figure 3-38 Problem 3-53