Three-Step Processes of Geometric and Vector Addition Part A - Position of the b

Question

Three-Step Processes of Geometric and Vector Addition Part A - Position of the boy Using the parallelogram law to add these vectors geometrically, determine the displacement of the boy relative to the tree (Figure 2) Learning Goal To be able to add and subtract vectors using geometric and vector addition Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x axis A brother and sister are playing in the woods when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled di-24.0 m at 1-20.50 from the tree then turned and traveled Hints 10.0 m at 2 1350 . Meanwhile, the sister traveled d3 18.5 m at an angle of 3--1 100 from the tree The angles are given with respect to east with counterclockwise being defined as positive m, Submit Give Up Figure1 012 Incorrect; Try Again; 5 attempts remaining Part B e, This question will be shown after you complete previous question(s) Part C This question will be shown after you complete previous question(s)

Explanation / Answer

displacement d1 = 24*cos20.5 i + 24*sin20.5 j

d1 = 22.5 i + 8.4 j

displacement d2 = 10*cos135 i + 10*sin135 j

d2 = -7.07 i + 7.07 j

db = d1 + d2 = 15.4i + 15.4 j

magnitude = sqrt(15.4^2+15.4^2) = 21.8 m

direction = tan^-1(15.4/15.4) = 45o

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