Question

A man travelling east at 8 km per hour find that the wind seems to blow directly from the north. On doubling the speed, he finds that it appears to come from N-E. Find the velocity of the wind and it's direction .

• A. $8\sqrt{2}$, its direction is from N-S.
• B. $8\sqrt{2}$, its direction is from N-W.
• C. $8\sqrt{2}$, its direction is from S-W.
• D. None of these

Answer 1

The correct option is B $8\sqrt{2}$, its direction is from N-W.

The velocity of wind relative to man $=$ Actual of wind $-$ Actual of man ...(1)
Let $i$ and $j$ represent unit vectors along East and North.
Let the actual velocity of wind be given by $xi+yj.$
In the 1st case the man's velocity is $8i$ and that of the wind relative to man being from north is $-pj$.
$\therefore -pj=(xi+yj)-8i$ by (1)
Comparing coefficients $x-8=0,y=-p$ ...(2)
In the 2nd case when the man doubles his speed, it seems to come from N-E.
$-q(i+j)=(xi+yj)-16i$

$\therefore x-16=-q,y=-q...\left(3\right)$
Putting $x=8$, we get $q=8$

$\therefore y=-8$

Hence the velocity of wind is $xi+yj=8(i-j)$
Its magnitude is $\sqrt{(8^2+8^2)}=8\sqrt{2}$ and $\tan \theta =-1\therefore \theta =-{45}^{\circ },$
Hence its direction is from N-W.