A bank in downtown Boston is robbed (see the map in the figure). To elude police

Question

A bank in downtown Boston is robbed (see the map in the figure). To elude police, the robbers escape by displacements: 32 km, 45° south of east; 53 km, 26° north of west;26 km, 18° east of south At the end of the third flight they are captured. In what town are they apprehended? helicopter, making three successive flights described by the following BOSTON and Vicinity Salem. 5 10 km Wobur exington Lynn Bank lington Medford Waltham Winthrop Newton Boso Massachusets BOSTON Brookline Bay Wellesley Framingham Dedham Quincy Weymouth Walpole

Explanation / Answer

Lets resolve the vector A into components

angle from positive x axis, = -45.0

Ax = A * cos

= 32.0 * cos(-45.0)

= 22.6274 km

Ay = A * sin

= 32.0 * sin(-45.0)

= -22.6274 km

Lets resolve the vector B into components

angle from positive x axis, = 154.0

Bx = B * cos

= 53.0 * cos(154.0)

= -47.6361 km

By = B * sin

= 53.0 * sin(154.0)

= 23.2337 km

Lets resolve the vector C into components

angle from positive x axis, = -72.0

Cx = C * cos

= 26.0 * cos(-72.0)

= 8.0344 km

Cy = C * sin

= 26.0 * sin(-72.0)

= -24.7275 km

we have:

A = 22.6274i- 22.6274j

B = -47.6361i+ 23.2337j

C = 8.0344i- 24.7275j

R = A + B + C

R = (22.6274i- 22.6274j) + (-47.6361i+ 23.2337j) + (8.0344i- 24.7275j)

= (Ax + Bx + Cx)i + (Ay + By + Cy)j

= (22.6274 - 47.6361 + 8.0344)i + (-22.6274 + 23.2337 - 24.7275)j

= -16.9742i- 24.1212j

magnitude of R = sqrt (-16.9742^2 + -24.1212^2)

magnitude of R = 29.495 km

Since x component is negative and y component is also negative

It lies in the 3rd cordinate

angle = 180 + atan(|y/x|)

angle = 180 + atan(|-24.1212/-16.9742|)

angle = 215 degree

They might be apprehended in wellesley

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