Question

To a man walking due west with a speed of 4m/s,
wind appears to blow from the north-east, when he
increases his speed to 7m/s the wind appears to
blow from the north. Find velocity of wind with
respect to ground.
(1) V50
(2) 140
(3) V58
(4) 142
​

Answer 1

Velocity of wind with  respect to ground is 7.61m/s from    $tan^{-1} \frac{3}{7}$  direction east of north.

Consider positive x axis as i , negative axis as -i and positive y axis as j and negative y axis -j .

(Bold letters represent vector)

• Velcoity of man = Vm = -Vmj = -4i

Let velocity of wind with respect to ground =

• Vw = v1i +v2j

Initially velocity of wind with respect to man

• Vwm= Vw - Vm =  (v1 + 4 )i + v2j

Given the wind is in South west ( its from north east going towards south west)

Therefore, its in 3rd quadrant and makes 45degree with both axis.

In such a vector the i and j components will be equal.

• Therefore, - ( v1  + 4 ) = v2.

Now the man increases  his speed to 7m/s.

Then Vwm = ( v1 + 7 ) i + v2j , is in south ( from north ) = -j direction.

Hence

• v1 + 7 = 0 and Vwm = -v2j

• v2 = - ( -7 + 4 ) = 3

Therefore, velocity of wind wrt ground  =

• Vw = -7i + 3j.

Velocity of wind is  7.61m/s from    $tan^{-1} \frac{3}{7}$  direction east of north.

Answer 2

Velocity of wind with  respect to ground is 7.61m/s

EXPLANATION

We need to do this sum using vectors.

Velcoity of man = $V_{m}$ = -$V_{mj}$ = -4i

Let velocity of wind with respect to ground = $V_{w}$ = $V_{w1i}+V_{w2j}$

Initially velocity of wind with respect to man

$V_{wm}$=$V_{w}$ -$V_{m}$ =  ( $V_{w1}$+ 4 )i + $V_{w2}$ j

Given the wind is in South west

Therefore it lies in the 3rd quadrant and makes a degree of 45°

Thus, i and j components will be equal.

Therefore, - ( $V_{w1}$  + 4 ) = $V_{w2}$

Now according to the question,he increases  his speed to 7m/s.

Then $V_{wm}$ = ( $V_{w1}$+ 7 ) i + $V_{w2}$j , is in south  = -j direction.

Hence

$V_{w1}$ + 7 = 0 and $V_{wm}$ = -$V_{w2}$j

$V_{w2}$ = - ( -7 + 4 ) = 3

Therefore, velocity of wind wrt ground  =

$V_{w}$ = -7i + 3j.

Velocity of wind is  7.61m/s from direction east of north.