3. Components of a vector A}, ' ' Consider a vector A in a rectangular coordinate system, as shown on the right, _) _) _) A can be expressed as the sum of two vectors: Ax, parallel to the x-axis, and A3,, _, _, _) _, _, parallel to the y-axis. Mathematically, A = Ax + Ay, where Ax and A}, are the _, component vectors of A. AJr = Acos A), = sin tan = A y .I' AJr 6 = tan'l(Ay / Ax) (the inverse tangent function) Exercise 1: (a) Find the horizontal and vertical components of the displacement of a superhero who had own 150 m at a 120 angle with respect to the positive x-axis. (b) Suppose instead the superhero had leaped with a displacement having an x-component of 32.5 m and a y-component of 24.3 111. Find the magnitude and direction of the displacement vector. Exercise 2: A hiker begins a trip by rst walking 25.0 km 450 east of south from her base camp. On the second day she walks 40.0 km in a direction 300" east of north, at which point she discovers a forest ranger 's tower. a) Determine the components of the hiker's displacements in the rst and second days. b) Determine the components of the hiker's total displacement for the trip. c) Find the magnitude and direction of the displacement from base camp. Exercise 3: A map suggests that Atlanta is 730 miles in a direction 500" north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21 .0 west of north from Atlanta. The gure shows the location of these three cities. Modelling the Earth as at, use this information to nd the displacement from Dallas to Chicago. Exercise 4: The helicopter View in the gure shows two people pulling on a stubborn mule. F1 = 120 N. F2 = 80.0 N. Find (a) the single force that is equivalent to the two forces shown and (b) the force the ground would have to exert on the mule to make the net force equal to zero