Question

Suppose you walk 7.5m in a direction 20degrees west of north and then travel 17m in a direction 40degrees south of west. a) how far are you from your starting point in meters? b) what is the angle, in degrees, of the compass direction of a line connecting your starting point to your final position measured south of west? c) repeat a, but for the 2nd leg you walk 17m in a direction 40degrees north of east. d) repeat a, but now you first walk 7.5m in a direction 40degrees south of west and 17m in a direction 20degrees east of south

Answer 1

let East be +x axis

a)
r1 = -7.5*sin(20) i + 7.5*cos(20) j

= -2.57 i + 7.05 j

r2 = -17*cos(40) i - 17*sin(40) j

= -13 i - 10.9 j

R = r1 + r2

= (-2.57 - 13) i + (7.5 - 10.9) j

= -15.57 i - 3.4 j

|R| = sqrt(15.57^2 + 3.4^2)

= 15.94 m   <<<<<<------Answer

b)

theta = tan^-1(3.4/15.57)

= 12.3 degrees south of west <<<<<<------Answer

c)

r1 = -7.5*sin(20) i + 7.5*cos(20) j

= -2.57 i + 7.05 j

r2 = 17*cos(40) i + 17*sin(40) j

= 13 i + 10.9 j

R = r1 + r2

= (-2.57 + 13) i + (7.5 + 10.9) j

= 10.43 i + 18.4 j

|R| = sqrt(10.43^2 + 18.4^2)

= 21.1 m <<<<<<<<------------------------Answer

d) r1 = -7.5*cos(20) i - 7.5*sin(20) j

= -7.05 i -2.57 j

r2 = 17*sin(40) i - 17*cos(40) j

= 10.9 i - 13 j

R = r1 + r2

= (-7.05 i -2.57 j) + 10.9 i - 13 j

= (-7.05 + 10.9) i + (-2.57 - 13) j

= 3.85 i - 15.6 j

|R| = sqrt(3.85^2 + 15.6^2)

= 16.07 m <<<<<<<<------------------------Answer