Question
why is the first angle 45+270 And why us the second one 90?
Chapter 2 1 veci Example 2 Components of Displacement Vectors party for a missing child follows a search dog named Trooper. Trooper wanders a lot and makes many splacemt many different paths. Trooper eventually finds the child and the story has a happy ending, but his trial saiffs a on various legs seem to be truly convoluted. On one of the legs he walks 200.0 m southeast, then Some 300.0 m. On the third leg, he examines the scents carefully for 50.0 m in the direction 30 n the fourth leg. Trooper goes directly south for 80.0 m, picks up a fresh scent and turms 23 he runs ets on various legs north vectors in ve. Find the scalar components of Trooper's displacement vectors and his displacement Strategy west of component form for each leg r coordinate system with the positive x-axis in the direction of geographic east, with the geographic north. Explicitly, the unit vector i of the x-axis points east and the y-direction pointed to of the y-axis points north. Trooper makes five legs, so there are five displacement vectors. We start magnitudes and direction angles, then we use Equation 2.17 to find the scalar components by identi of the displacements and Equation 2.12 for the displacement vectors. Solution On the first I fying their 200.0 m and the direction is southeast. For direction eg, the displacement magnitude is ll measured angle we can take either 45° measured clockwise from the east direction or 45° + 270 direction. With the first choice, --45®. with the second choice, " +315". We can use either one of these two angles. The components are 1x = L1 cos ! = (200.0 m) cos 3 150-141.4 m, ,-Li sin ! = (200.0 m) sin 315° 141.4 m. The displacement vector of the first leg is ,-Llri + Livj = (141.4 i-141,4 j ) m. 300.0 m and the On the second leg of Trooper's wanderings, the magnitude of the displacement is direction is north. The direction angle is ,-+ 90° . We obtain the following results: L2 L2r L2y 12 cos 02= (300.0 m) cos 90°=0.0 , L2 sin 02 = (3000 m) sin 90-300.0 m, - the third leg, the displacement magnitude is L3 50.0 m and the direction is 30° west of north. Th ction angle measured counterclockwise from the eastem direction is 3 = 30° + 90° + 120° . This giv ollowing answers L3x 3y L3 cos ,-(50.0 m) cos l20°=-25.0 m, L3 sin 6, = (50.0 m)sin 120°= +43.3 m, - L 3 = L3x i + L3x j = (-25.0 i +43.3 j )m. fourth leg of the excursion, the displacement magnitude is L4 80.0m and the direction is south. n angle can be taken as either .--90° or ,-+270° . We obtain
Explanation / Answer
If you make a coordinate system in which east direction is alomg positive x axis, then southeast direction makes an angle 45o with x axis or east when measured clock wise, but same line measures 270 + 45o when measured in anti clockwise.
As in our coordinate system, north direction is along y axis, positive, hence, y axis positive direction makes a 90o amgle witj x azis positive direction. Thats why angle is 90o in this case
