Chapter 3 - 3.1 We are given that. When two vectors are...

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3.1 We are given that. When two vectors are added graphically, the second vector is positioned with its tail at the tip of the first vector. The resultant then runs from the tail of the first vector to the tip of the second vector. In this case, vector will be positioned with its tail at the origin and its tip at the point (0, 29). The resultant is then drawn, starting at the origin (tail of first vector) and going 14 units in the negative y -direction to the point (0, - 14). The second vector, , must then start from the tip of at point (0, 29) and end on the tip of at point (0, - 14) as shown in the sketch at the right. From this, it is seen that 3.3 (a) In your vector diagram, place the tail of vector at the
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tip of vector . The vector sum, , is then found as shown in the vector diagram and should be (b) To find the vector difference, form the vector (same magnitude as , opposite direction) and add it to vector as shown in the diagram. You should find that
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3.4 Sketches of the scale drawings needed for parts (a) through (d) are given below. Following the sketches 3.7 Using a vector diagram, drawn to scale, like that shown at the right, the final displacement of the plane can be found to be. The requested displacement of the base from point B is , which has the same magnitude but the opposite direction. Thus, the answer is 3.8 Your vector diagram should look like the 3.14 (a) The resultant displacement is , where , due north, , due east, , and due south. Choosing east as the positive x -direction and north as the positive y -direction, we find the components of the resultant to be
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and The magnitude and direction of the resultant are then and Thus, . (b) Because of the commutative property of vector addition, the net displacement is the same regardless of the order in which the individual displacements are executed. 3.15 3.17 After 3.00 h moving at 41.0 km/h, the hurricane is 123 km at 60.0° N of W from the island. In the next 1.50 h, it travels 37.5 km due north. The components of these two displacements are as follows: Displacement x -component (eastward) y -component (northward) 123 km - 61.5 km + 107 km 37.5 km 0 + 37.5 km Resultant - 61.5 km 144 km Therefore, the eye of the hurricane is now
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3.19 The components of the displacements , , and are and Thus, , and so , and
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City C is from the starting point. 3.23 (a) With the origin chosen at point O as shown in Figure P3.23, the coordinates of the original position of the stone are. (b)
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Chapter 3 - 3.1 We are given that. When two vectors are...

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