352 Basic Engineering Mathematics
(b) 146 cm 2 (vi) (a) 86.5 cm 3 (b) 142 cm 2
(vii) (a) 805 cm 3 (b) 539 cm 2
7. (a) 17.9 cm (b) 38.0 cm
8. 125 cm 3
9. 10.3 m 3 , 25.5 m 2
10. 6560 litres
11. 657.1 cm 3 , 1027 cm 2
12. 220.7 cm 3
13. (a) 1458 litres (b) 9.77 m 2 (c) £140.45
Exercise 108 (page 255)
1. 147 cm 3 , 164 cm 2
2. 403 cm 3 , 337 cm 2
3. 10480 m 3 , 1852 m 2
4. 1707 cm 2
5. 10.69 cm
6. 55910 cm 3 , 6051 cm 2
7. 5.14 m
Exercise 109 (page 256)
1. 8 : 125 2. 137.2 g
Chapter 28
Exercise 110 (page 259)
1. 4.5 square units 2. 54.7 square units 3. 63.33 m
4. 4.70 ha
5. 143 m
2
Exercise 111 (page 260)
1. 42.59 m 3
2. 147 m 3
3. 20.42 m 3
Exercise 112 (page 263)
1. (a) 2 A (b) 50 V (c) 2.5 A
2. (a) 2.5 V (b) 3 A
3. 0.093 As, 3.1 A
4. (a) 31.83 V (b) 0
5. 49.13 cm
2
, 368.5 kPa
Chapter 29
Exercise 113 (page 266)
1. A scalar quantity has magnitude only; a vector
quantity has both magnitude and direction.
2. scalar
3. scalar
4. vector 5. scalar
6. scalar
7. vector 8. scalar
9. vector
Exercise 114 (page 273)
1. 17.35 N at 18.00 ◦ to the 12 N force
2. 13 m/s at 22.62 ◦ to the 12 m/s velocity
3. 16.40 N at 37.57 ◦ to the 13 N force
4. 28.43 N at 129.30 ◦ to the 18 N force
5. 32.31 m at 21.80 ◦ to the 30 m displacement
6. 14.72 N at −14.72
◦ to the 5 N force
7. 29.15 m/s at 29.04 ◦ to the horizontal
8. 9.28 N at 16.70 ◦
9. 6.89 m/s at 159.56 ◦
10. 15.62 N at 26.33 ◦ to the 10 N force
11. 21.07 knots, E 9.22 ◦ S
Exercise 115 (page 276)
1. (a) 54.0 N at 78.16
◦ (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 116 (page 277)
1. 83.5 km/h at 71.6
◦ to the vertical
2. 4 minutes 55 seconds, 60 ◦
3. 22.79 km/h, E 9.78 ◦ N
Exercise 117 (page 277)
1. i − j − 4k
2. 4i + j − 6k
3. −i + 7j − k
4. 5i − 10k
5. −3i + 27j − 8k
6. −5i + 10k
7. i + 7.5j − 4k
8. 20.5j − 10k
9. 3.6i + 4.4j − 6.9k
10. 2i + 40j − 43k
Chapter 30
Exercise 118 (page 279)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395)
Exercise 119 (page 281)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395)
Exercise 120 (page 283)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395) 4. 11.11 sin(ωt + 0.324)
5. 8.73 sin(ωt − 0.173)
(b) 146 cm 2 (vi) (a) 86.5 cm 3 (b) 142 cm 2
(vii) (a) 805 cm 3 (b) 539 cm 2
7. (a) 17.9 cm (b) 38.0 cm
8. 125 cm 3
9. 10.3 m 3 , 25.5 m 2
10. 6560 litres
11. 657.1 cm 3 , 1027 cm 2
12. 220.7 cm 3
13. (a) 1458 litres (b) 9.77 m 2 (c) £140.45
Exercise 108 (page 255)
1. 147 cm 3 , 164 cm 2
2. 403 cm 3 , 337 cm 2
3. 10480 m 3 , 1852 m 2
4. 1707 cm 2
5. 10.69 cm
6. 55910 cm 3 , 6051 cm 2
7. 5.14 m
Exercise 109 (page 256)
1. 8 : 125 2. 137.2 g
Chapter 28
Exercise 110 (page 259)
1. 4.5 square units 2. 54.7 square units 3. 63.33 m
4. 4.70 ha
5. 143 m
2
Exercise 111 (page 260)
1. 42.59 m 3
2. 147 m 3
3. 20.42 m 3
Exercise 112 (page 263)
1. (a) 2 A (b) 50 V (c) 2.5 A
2. (a) 2.5 V (b) 3 A
3. 0.093 As, 3.1 A
4. (a) 31.83 V (b) 0
5. 49.13 cm
2
, 368.5 kPa
Chapter 29
Exercise 113 (page 266)
1. A scalar quantity has magnitude only; a vector
quantity has both magnitude and direction.
2. scalar
3. scalar
4. vector 5. scalar
6. scalar
7. vector 8. scalar
9. vector
Exercise 114 (page 273)
1. 17.35 N at 18.00 ◦ to the 12 N force
2. 13 m/s at 22.62 ◦ to the 12 m/s velocity
3. 16.40 N at 37.57 ◦ to the 13 N force
4. 28.43 N at 129.30 ◦ to the 18 N force
5. 32.31 m at 21.80 ◦ to the 30 m displacement
6. 14.72 N at −14.72
◦ to the 5 N force
7. 29.15 m/s at 29.04 ◦ to the horizontal
8. 9.28 N at 16.70 ◦
9. 6.89 m/s at 159.56 ◦
10. 15.62 N at 26.33 ◦ to the 10 N force
11. 21.07 knots, E 9.22 ◦ S
Exercise 115 (page 276)
1. (a) 54.0 N at 78.16
◦ (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 116 (page 277)
1. 83.5 km/h at 71.6
◦ to the vertical
2. 4 minutes 55 seconds, 60 ◦
3. 22.79 km/h, E 9.78 ◦ N
Exercise 117 (page 277)
1. i − j − 4k
2. 4i + j − 6k
3. −i + 7j − k
4. 5i − 10k
5. −3i + 27j − 8k
6. −5i + 10k
7. i + 7.5j − 4k
8. 20.5j − 10k
9. 3.6i + 4.4j − 6.9k
10. 2i + 40j − 43k
Chapter 30
Exercise 118 (page 279)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395)
Exercise 119 (page 281)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395)
Exercise 120 (page 283)
1. 4.5 sin(A + 63.5 ◦ )
2. (a) 20.9 sin(ωt + 0.62) volts
(b) 12.5 sin(ωt − 1.33) volts
3. 13 sin(ωt + 0.395) 4. 11.11 sin(ωt + 0.324)
5. 8.73 sin(ωt − 0.173)