Question

A person walks 30m due north, then 50m at 35 degrees. Find their total displacement.

Answer 1

Using the cosine rule (a^2 = b^2 + c^2 - 2bc cos A), we can work out the displacement:
Displacement = a
b = 30
c = 50
A = 180 - 35 = 145 degrees.

a^2= 900 + 2500 -1500*-0.81915...
= 3400 + 1228.728...
= 4628.72...
a = 68.034...
= 68.0m (to 3s.f.).

To work out the angle from starting place, use another configuration of the cosine rule:

`cos(C)= (a^(2) +b^(2)- c^(2) )/(2ab)`:
cos (C)=
`(4628.72...+900-2500)/(2*68*30)`
= 3028.7.../4080
= 0.7423...
C = 42.069... degrees
= 042 bearing