Answer to Question #260864 in Physics for jon

Question

An airplane trip involves four legs, with three stopover the first leg is due north 620 Km, the second leg is south east 45^o for 440 Km, third leg is at 53^o south of west for 550 Km, and fourth leg is due               north 20km, what is the plane total displacement and direction?      

Answer 1

Determine the components of total displacement:

$$d_N=620-440\sin45°-550\sin53°=-130\text{ km},\\ d_W=0-440\cos45°+550\cos53°=-111\text{ km},\\ d=\sqrt{d_N^2+d_W^2}=171\text{ km}.\\\space\\ \theta=\arctan\bigg|\frac{d_N}{d_W}\bigg|=49.5°\text{S of W. }$$