Answers to exercises
Exercise 96 (Page 203)
3. i = 21.79 sin(ωt − 0.639) A
1. 193 km
4. v = 5.695 sin(ωt + 0.670) V
2. (a) 122.6 m (b) 94◦ 49 , 40◦ 39 , 44◦ 32
5. x = 14.38 sin(ωt + 1.444) cm
3. (a) 11.4 m
6. 13 sin(ωt + 1.176) mA
(b) 17◦ 33
4. 163.4 m
Exercise 103 (Page 218)
5. BF = 3.9 m, EB = 4.0 m
1. 21, 25
2. 48, 96
5. 50, 65
6. 0.001, 0.0001
6. 6.35 m, 5.37 m
7. 32.48 A, 14◦ 19
3. 14, 7
4. −3, −8
7. 54, 79
Exercise 104 (Page 219)
Exercise 97 (Page 205) 1. 80◦ 25 , 59◦ 23 , 40◦ 12
2. (a) 15.23 m
(b) 38◦ 4
3. 40.25 cm, 126◦ 3
4. 19.8 cm
5. 36.2 m
6. x = 69.3 mm, y = 142 mm
7. 130◦
8. 13.66 mm
1. 1, 3, 5, 7, …
2. 7, 10, 13, 16, 19, …
3. 6, 11, 16, 21, …
4. 5n
5. 6n − 2
6. 2n + 1
7. 4n − 2
8. 3n + 6
9. 63 (= 216), 73 (= 343) Exercise 105 (Page 220)
Exercise 98 (Page 210)
1. 68
2. 6.2
3. 85.25
5. 11
6. 209
7. 346.5
1. 47 N at 29◦
2. Zero
3. 7.27 m/s at 90.8◦
4. 6.24 N at 76.10◦
5. 2.46 N, 4.12 N
6. 5.7 m/s2 at 310◦
Exercise 106 (Page 222)
7. 11.85 A at 31.14◦
8. 15.62 N at 26.33◦ to the 10 N force
1. − 12 5.
9. 8.50 km/h at 41.73◦ E of S
8 12 ,
2. 1 12 , 3, 4 12 12,
6. (a) 120
4. 25
(b) 26070
(c) 250.5 8. £8720
(b) 45.64 N at 4.66◦
2. (a) 31.71 m/s at 121.81◦ (b) 19.55 m/s at 8.63◦ Exercise 100 (Page 213) 1. 83.5 km/h at 71.6◦ to the vertical 2. 4 minutes 55 seconds
3. 7808
19
7. £10000, £109500
Exercise 99 (Page 212) 1. (a) 54.0 N at 78.16◦
15 12 ,
4. 23 12
3. 23.18 m/s at 72.24◦ E of S
Exercise 107 (Page 223) 1. 2560
2. 273.25
3. 512, 4096
5. 812.5
6. 8
7. 1 23
4. 10th
Exercise 108 (Page 225) 1. (a) 3
(b) 2
(c) 59022
2. £1566, 11 years
Exercise 101 (Page 215)
3. 48.71 M 4. 71.53 g 5. (a) £599.14
1. 4.5 sin(A + 63.5◦ )
6. 100, 139, 193, 268, 373, 518, 720, 1000 rev/min
2. (a) 20.9 sin(ωt + 0.62) volts 3. 13 sin(ωt + 0.395)
(b) 12.5 sin(ωt − 1.33) volts
(b) 19 years
Exercise 109 (Page 226) 1. (a) continuous
(b) continuous (c) discrete
(d) continuous Exercise 102 (Page 217) 1. 11.11 sin(ωt + 0.324) 2. 8.73 sin(ωt − 0.173)
2. (a) discrete (d) discrete
(b) continuous
(c) discrete
281