chapter 6 practice masters answers …blm 6-12. . page1)...blm 6-12 chapter 6 practice masters...
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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
Chapter 6 Practice Masters Answers …BLM 6-12. . (page 2)
Calculus and Vectors 12: Teacher's Resource Copyright © 2008 McGraw-Hill Ryerson Limited BLM 6-12 Chapter 6 Practice Masters Answers
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)
Chapter 6 Practice Masters Answers …BLM 6-12. . (page 3)
Calculus and Vectors 12: Teacher's Resource Copyright © 2008 McGraw-Hill Ryerson Limited BLM 6-12 Chapter 6 Practice Masters Answers
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
Chapter 6 Practice Masters Answers …BLM 6-12. . (page 4)
Calculus and Vectors 12: Teacher's Resource Copyright © 2008 McGraw-Hill Ryerson Limited BLM 6-12 Chapter 6 Practice Masters Answers
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