CH 3 Vectors in Physics 3-1 Scalars Versus Vectors What quantity or quantities from Chapter 2 are scalars? What quantity or quantities from Chapter 2 need to be expressed as vectors?

3.54 miles 5 miles 3-2 The Components of a Vector

Ch3: Vectors 3-2 The Components of a Vector x y r  rxrx ryry r x = r cos  r y = r sin  x y r  cos  = x/r sin  = y/r tan  = y/x Right Angle Trigonometry  = tan -1 (r y /r x ) r = (r x 2 + r y 2 ) 1/2

r x = miles r y = 3.54 miles 5 miles x y  = 135° 3-2 The Components of a Vector

P3.4 (p. 75)

D H R P3.6 (p. 75)

3.54 miles 5 miles 3-3 Adding and Subtracting Vectors A C B A + B = C A + B  C  5

CT1: Which vectors are equal? Choose the best answer. A. A and G B. G and J C. I and L D. Answers A, B and C are all correct. E. None of the answers is correct.

3-3 Adding and Subtracting Vectors A. Graphical Draw vector lengths to scale and use a protractor for angles Addition of vectors Negative of a vector Subtraction of vectors

CT2: Which vectors are the negative of each other? Choose the best answer. A. A and G B. G and J C. C and D D. B and E E. H and K

ABCDEF Concept Test 3

3-3 Adding and Subtracting Vectors B. Using Vector Components Addition of vectors Subtraction of vectors P3.18 (p. 76)

3-4 Unit Vectors

Before Class Assignment 2/6/2008 q3-1 19/19 correct q correct 3 wrong 3 no explanation

Before Class Assignment 2/6/2008 Read some responses

A.A. B.B. C.C. D. E. F. Concept Test 5

If A = 3x + 4y and B = x – 2y, then C = 2A – B is A. 7x + 10y B. 5x + 6y C. 5x + 10y D. 7x + 6y E. 4x + 2y F. 4x + 6y                     Concept Test 4

P3.25 (p. 76)

3-5 Position, Displacement, Velocity, and Acceleration as Vectors

CT 6: Which graph represents a constant acceleration? A B vxvx t t vxvx

x y CT7: For the following path with constant speed (black circle), the red vector is a(an) A. Position B. Velocity C. Acceleration for the particle represented by the green dot.

x y CT 8: For the following path with constant speed (black circle), the red vector is a(an) A. Position B. Velocity C. Acceleration for the particle represented by the green dot.

x y CT9: For the following path with constant speed (black circle), the red vector is a(an) A. Position B. Velocity C. Acceleration for the particle represented by the green dot.

3-5 Position, Displacement, Velocity, and Acceleration as Vectors P3.37 (p. 77) P3.33 (p. 77)

3-6 Relative Motion P3.41 (p. 77) CT10: What do I do with 1.22 and 16.5? A.Add B.Subtract P3.45 (p. 77)

CT11 P3.45c: If the pilot decreases the air speed of the plane, but still wants to head due north should the angle found in part a be increased or decreased? A. increased B. decreased

CT12 Ex3-2 Crossing a River: What angle is closest to the angle that will take the boat straight across the river (or perpendicular to the current)? Measure angle with respect to the + x axis. A. 20° B. 13° C. 0° D. -13° E. -20°