To be able to add and subtract vectors using geometric and vector addition. A br

Question

To be able to add and subtract vectors using geometric and vector addition.

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 d1=21.0 m at 1=21.0 from the tree then turned and traveled d2=10.5 m at 2=134. Meanwhile, the sister traveled d3=19.0 m at an angle of 3=120 from the tree. The angles are given with respect to east with counterclockwise being defined as positive

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)

Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x axis.

b)Using the method of vector addition by components, determine the displacement from the boy to the girl.(Figure 3)

c)After the boy has found his sister, they want to travel the shortest path home. If their home is located d4=100 m due north of the big tree, what is the magnitude and direction of the displacement from the siblings to their home, dBGH ? (figure 4)

Explanation / Answer

(A) d_boy = 21(cos21i + sin21j) + 10.5 cos(134i + sin134j)

d_boy = 12.3i + 15.1j

distance = sqrt(12.3^2 + 15.1^2)

= 19.5 m

angle = tan^-1(15.1 / 12.3) = 51 deg

Ans: 19.5 m , 51 deg

(B) r_girl = 19 cos(360 - 120)i + 19 sin(360 - 120)j

= -9.5i - 16.5j

from boy to girl = (-9.5 - 12.3)i + (-16.5 -15.1)j

= - 21.8i - 31.6j

distance = sqrt(21.8^2 + 31.6^2) = 38.4 m

theta = tan^-1(31.6 / 21.8) + 180 = 235 deg

Ans : 38.4 m , 235 deg

(C) d = (0i + 100j) - ( -9.5i - 16.5j )

d = 9.5i + 116.5j

|d| = sqrt(9.5^2 + 116.5^2) = 116.9 m

theta = tan^-1(116.5 / 9.5) = 85 deg

Ans: 116.9 m, 85 deg

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