A cyclist travels a distance of 1200m due north before going 2000m due east followed by 500m south-west. Draw a scale diagram to calculate the cyclist's final displacement form her initial position?

Answer 1

D = 1200m[90o] + 2000[0] + 500[225].

X = 1200*Cos90 + 2000*Cos0 + 500*Cos225 =
0 + 2000 - 354 = 1646 m.

Y = 1200*sin90 + 2000*sin0 + 500*sin225 =
1200 + 0 - 354 = 846 m.

Tan A = Y/X = 846/1646 = 0.51397.
A =

D = X/Cos A.