CH 3 Vectors in Physics3-1 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

3.5

4 m

iles

5 miles

3-2 The Components of a Vector

Ch3: Vectors3-2 The Components of a Vector

x

y

r

rx

ryrx = r cos ry = r sin

x

yr

cos = x/r

sin = y/r

tan = y/x

Right Angle Trigonometry

= tan-1(ry/rx)

r = (rx2 + ry

2)1/2

rx = -3.54 miles

r y =

3.5

4 m

iles

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

3.5

4 m

iles

5 miles

3-3 Adding and Subtracting Vectors

A

C

BA + B = C

A + B C3.54 + 3.54 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 VectorsA. 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

A B C D E F

Concept Test 3

3-3 Adding and Subtracting VectorsB. 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• q3-2 16 correct

3 wrong 3 no explanation

Before Class Assignment 2/6/2008

Read some responses

A.B.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

vx

t t

vx

x

y

CT7: For the following path with constant speed (black circle), the red vector is a(an)

A. PositionB. 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. PositionB. 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. PositionB. Velocity C. Accelerationfor 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 MotionP3.41 (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. increasedB. 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°