Chapter 6 Practice Masters Answers …BLM 6-12. . page1)...BLM 6-12 Chapter 6 Practice Masters Answers Prerequisite Skills 1. 2. Answers may vary. For example: a) 1 cm : 100 km b)

Chapter 6 Practice Masters Answers …BLM 6-12. . (page 1)

Calculus and Vectors 12: Teacher's Resource Copyright © 2008 McGraw-Hill Ryerson Limited BLM 6-12 Chapter 6 Practice Masters Answers

Prerequisite Skills 1.

2. Answers may vary. For example: a) 1 cm : 100 km b) 1 cm : 150 mm c) 1 cm : 5 cm d) 1 cm : 1000 km 3. a) 30° b) 107° c) 120° 4. 26.3 cm 5. 20.1° 6. 72.9 cm 7. 57.8° 8. a) 61.5 cm b) 33.3° c) 60.2° 9. a) Pratheep: 10 272.8 m; Tenzin: 7817.6 m b) 6324.5 m 10. a) 2b b) 0 c) 8 d) ab2 + 2abc + ac2

6.1 Introduction to Vectors 1. a) scalar b) scalar c) vector d) vector e) scalar f) vector 2. a) 180 N to the right b) 50 km/h at 30° above the horizontal 3. a) N65°E b) S60°E c) S55°W d) W e) N50°W f) N17°E 4. a) 40° b) 115° c) 212° d) 333° e) 234° f) 349° 5. Diagrams may vary. For example, in the diagram shown, IJ

ur

is parallel to AB

u ru

, KL

u ru

is opposite to AB

u ru

, and MN

u ruu

is equivalent

to AB

u ru

.

6. a) AB

u ru

= ED

u ru

, BC

u ru

= FE

uru

, CD

u ru

= AF

u ru

,

DE

u ru

= BA

u ruu

, EF

uru

= CB

u ru

, FA

u ru

= CD

u ru

,

FB

u ru

= EC

u ru

, BF

u ru

= CE

u ru

b) AB

u ru

= DC

u ru

, BA

u ruu

= CD

u ru

, AD

u ruu

= BC

u ru

,

DA

u ruu

= CB

u ru

, DE

u ru

= EB

u ru

, BE

u ru

= ED

u ru

,

AE

u ru

= EC

u ru

, CE

u ru

= EA

u ru

7. a) 300 km south b) 700 N on a bearing of 300°

c) 180 km/h on a quadrant bearing of N25°E 8. Diagrams may vary. a)

b) c)

d) e)

9. a) DC

u ru

b) none c) none d) DE

u ru

6.2 Addition and Subtraction of Vectors 1. a)

b) c)

d)

2. a) w

r

= vr

– ur

b) QR

u ru

= PR

u ru

– PQ

u ru



3.

4. a)

b)

c)

d)

5. a) EB

u ru

b) BD

u ru

c) ED

u ru

d) CB

u ru

6. a)

b) 17.9 m/s2, 33.2° from the horizontal 7. 1932.4 km N10.7°W

6.3 Multiplying a Vector by a Scalar 1. Diagrams may vary. For example,

2. a) 7 a

r

b) 5 u

r

+ 13 v

r

c) – u

r

+ 8 v

r

d) 7 u

r

+ 7 v

r

e) – u

r

– 5 v

r

f) ur

+ 27 v

r

3. a)

b)

c)

d)



4. a)

b)

c)

5. a) 2 v

r

b) ur

c) 2 u

r

d) ur

+ vr

e) 2 u

r

+ 2 v

r

f) ur

+ 2 v

r

g) 2 v

r

– 2 u

r

6.4 Applications of Vector Addition 1. a) 58.7 km/h at S66.9°W b) 45 m/s west c) 68.0 m at 19.8° above the horizontal d) 8.0 N at N64.1°E e) 92.2 km at N79.5°E 2. 15 N N53°W or 307° 3. a) 44 N b) 153 N 4. a) Diagrams may vary. For example,

b)

T

1

ur

= 105.5 N, T

2

ur

= 41.7 N 5. 74.1 N 6.

T

1

ur

= 202.9 N, T

2

ur

= 52.5 N

7. a) Diagrams may vary. For example,

b) 622.0 km/h at a bearing of 328° 8. a) Diagrams may vary. For example,

b) S54.4°E c) 15.9 knots 9. a) Diagrams may vary. For example,

b) 2.6 km/h at an angle of 32.2° with the adjacent shore c) 1.7 km 6.5 Resolution of Vectors Into Rectangular Components

1. a) F

ur

h = 455.2 N;

F

ur

v = 343.0 N

b) F

ur

h = 17.9 N;

F

ur

v = –22.9 N

c) F

ur

h = 586.8 N;

F

ur

v = 1103.7 N

d) F

ur

h = –90.7 N;

F

ur

v = 363.9

2. rate of climb: 1.0 m/s; horizontal groundspeed: 3.9 m/s 3. a) 171.0 km/h b) 469.8 km/h 4. forward: 303.1 N; upward: 212.2 N 5.

R

1

ur

= 32 635.2 N; R

2

uru

= 22 323.8 N 6. parallel: 225.0 N; perpendicular: 47.8 N 7. vertical: 4399.9 N; horizontal: 16 420.7 N 8. a) 106.5 N b) 74.6 N 9. 41 N is 28.4° from 50 N; 24 N is 54.5° from 50 N



10. 507.2 m/s at 9.6° from the horizontal 11. rate of climb: 248.0 km/h; horizontal groundspeed: 681.3 km/h Chapter 6 Review 1. a) S21°E b) N64°E c) N80°W d) S22°W 2. Diagrams may vary. a) b)

c)

3. a) AF

u ru

b) AC

u ru

c) DE

u ru

d) BD

u ru

e) ED

u ru

f) BE

u ru

4. a) 183.0 N b) 10.6 N c) 92.2 N 5. a)

b)

c)

d)

6. 459.5 N; 567.8 N 7. tension: 973.6 N; compression: 1691.0 N 8. 164.4 N Practice Test 1. B 2. D 3. a) b)

4. a) EA

u ru

b) BA

u ruu

c) AC

u ru

5. a)

1

2AC

u ru

b)

AB

u ru

+1

2BC

u ru

c) 2AF

u ru

– 2EC

u ru

6. 387.1 N, 54.5° from the direction of the boards 7. 813.8 km/h at a bearing of 229.3° 8. 3.9 N 9. 44.5 N 10. S23.9°E, 644.2 km/h 11. 6.8 N, 42.7° from resultant 12. 328.8 N and 246.6 N

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Chapter 6 Practice Masters Answers …BLM 6-12. . page1)...BLM 6-12 Chapter 6 Practice Masters Answers Prerequisite Skills 1. 2. Answers may vary. For example: a) 1 cm : 100 km b)