A 180 cos 30i direction magnitude sin 30j arctan

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Unformatted text preview: 40.18 newtons —CONTINUED— Section 10.1 Vectors in the Plane 231 79. —CONTINUED— (c) M 0 455 0 (d) 500 30 440.2 11.8 60 396.9 23.1 50 90 328.7 33.2 120 241.9 40.1 150 149.3 37.1 180 95 0 (e) M decreases because the forces change from acting in the same direction to acting in the opposite direction as increases from 0 to 180 . M α 0 0 180 0 0 180 81. F1 F2 F3 75 cos 30 i 75 2 3 F2 F2 F3 75 sin 30 j 125 i 2 228.5 lb 100 cos 45 i 75 2 50 2 100 sin 45 j 125 2 3j 125 cos 120 i 125 sin 120 j 50 2 F3 71.3 R R F1 F1 83. (a) The forces act along the same direction. 0. (b) The forces cancel out each other. 180 . (c) No, the magnitude of the resultant can not be greater than the sum. 85. 4, 1 , 6, 5 , 10, 3 y 8 6 4 2 2 4 8 y 8 y (8, 4) (1, 2) (3, 1) 6 8 x 6 4 2 −4 −2 −2 −4 2 (6, 5) (1, 2) (3, 1) 4 6 (8, 4) 6 4 2 x (1, 2) (8, 4) (10, 3) x (− 4, −1) −4 8 −2 −2 −4 (3, 1) 4 6 8 10 87. u v → CB → CA u cos 30 i v cos 130 i sin 30 j sin 130 j v sin 130 v cos 130 2000 0 A 50° v y 130° 30° B u C x Vertical components: u sin 30 Horizontal components: u cos 30 Solving this system, you obtain u 1305.5 and v 1758.8. 30° 89. Horizontal component Vertical component v cos v sin 1200 cos 6 1200 sin 6 1193.43 ft sec 125.43 ft sec 232 91. Chapter 10 u v u v Vectors and the Geometry of Space sin 148 j sin 45 j 100 cos 45 i 547.64 j 38.34 . 547.64 2 900 cos 148 i 100 cos 45 i 900 cos 148 692.53 i arctan 900 sin 148 100 sin 45 j 547.64 692.53 692.53 2 38.34 North of West. 882.9 km hr. u 93. F1 v F2 F3 0 sin 35 j 0 3600 T3 sin 92 3600 and T3 0.97495 3600 ⇒ T3 3692.48 T3 cos 92 i sin 92 j 0 3600j T2 cos 35 T2 cos 35 T2 T2 cos 35 i T3 cos 92 T3 sin 92 T3 cos 92 T cos 92 ⇒3 sin 35 cos 35 cos 35 Finally, T2 157.32 95. Let the triangle have vertices at 0, 0 , a, 0 , and b, c . Let u be the vector joining 0, 0 and b, c , as indicated in the figure. Then v, the vector joining the midpoints, is v a 2 b i 2 97. w uv c j 2 vu vi u y (b, c) c (a + b , 2( 2 v b a c j i 2 2 1 bi cj 2 u 1 u 2 x (0, 0) a ( 2 , 0( (a, 0) u v cos v sin v vj u v u...
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