Answer to Question #254631 in Classical Mechanics for aza

Question

A truck is moving north at a speed of 70 km/h. The exhaust pipe above the truck sends out a trail of smoke that makes an angle of 20o east of south behind the truck. If the wind is blowing directly toward the east, what is the wind speed at that location?

Answer 1

$\text{let }\vec{OA} -\text{smoke trail}$

$\text{visible to the observer from above after some time t}$

$\angle (\vec{NS},\vec{OA})= 20\degree$

$\vec{OA} = \vec{OH} +\vec{HA}$

$\vec{OH}\text{ car speed}$

$\vec{HA}\text{ vind speed}$

$\tan\angle (\vec{NS},\vec{OA})= \frac{|\vec{HA}|}{|\vec{OH}|}$

$|\vec{OH}|=\tan\angle (\vec{NS},\vec{OA})*|\vec{HA}|=70*\tan20\degree=25.47\frac{km}{h}$

$\text{Answer:} 25.47\frac{km}{h}$