Question

A bus moving at a constant speed of 12km/h travels east for 0.67 hrs then 20 degrees east of north fork 0.33 hrs and finally went west for 0.5 hrs what is the bus velocity

Answer 1

Average velocity is the total displacement divided by elapsed time.

Resolve the distance of 20 degrees east of north:

$$d_{y}=12\cdot0.33\text{ cos}20°=3.72\text{ km North}\\ d_{x}=12\cdot0.33\text{ sin}20°=1.35\text{ km East}$$

Therefore, the total displacement is

$$D_x=12\cdot0.67+1.35-12\cdot0.5=3.39\text{ km},\\ D_y=0+3.72+0=3.72\text{ km},\\ D=\sqrt{D_x^2+D_y^2}=\sqrt{3.39^2+3.72^2}=5.03\text{ km}.$$

The average velocity is

$$v=\frac{5.03}{0.67+0.33+0.5}=3.35\text{ km/h}.$$