Question

A person travelling towards east at the rate of 2 m/sec finds that the wind seems to blow directly from the north, on doubling his speed it appears to come from the north east. Find the magnitude and direction of the wind.

Answer 1

Using +x = east and +y = north

Suppose velocity of wind is (X,Y).

Velocity of person, V = (2,0)

Velocity of wind relative to person = (X,Y) - (2,0) = (X-2,Y)

Since wind appears to blow directly from the north, the east-west component (X-2) must be zero.

$X-2=0$

$X=2km/hr$

Velocity of person, V=(4,0)

Velocity of wind relative to person = (X,Y) - (4,0) = (X-4,Y) = (-2,Y)

Since relative velocity is from the north east ( direction south west ), this is an angle of ${\tan }^{-1}1={45}^o$ ( south of west )

The x and y components of the relative velocity must be equal, because $\tan {45}^o=1$

So, $Y=-2km/hr$

Wind vector = $(2,-2)km/hr$

Wind velocity = $\sqrt{2^2+2^2}=2.8km/hr$

Direction to the south east ( from the north west )