Question

A man walking eastwards at 5m/s observes that wind is blowing from the north.On doubling his speed eastward he observes that wind is blowing from north-east.Find the velocity of the wind.

Answer 1

Answer: 7.07 m/s

Let the velocity of the wind be (x, y)  

Velocity of the man be (5, 0)  

Velocity of the wind with respect to the man = (x, y) - (5, 0) = (x-5, y)  

Given that the wind blows from north direction. Therefor the east-west aspect of the wind will be zero which means,  

                                x - 5 = 0  

                                x = 5 m/sec  

Similarly, when the velocity of the man is doubled, that is (10, 0), then the speed of the wind with respect to the man is,

                                (x, y) - (10, 0) = (x - 10, y)  

Substituting the value of x,

                                (5 - 10, y) = (-5, Y)  

Relative velocity is from the north east direction.

[IMG]:

Where the angle of tan-1 (1) = 45° to the direction south west  

Hence y = -5 m/sec  

The vector equivalent of wind = (5, -5)  

                           $Wind\quad velocity\quad =\quad \sqrt { { 5 }^{ 2 }+{ 5 }^{ 2 } } \\=\sqrt { 25+25 } \\=\sqrt { 50 }\\Wind\quad velocity\quad =\quad 7.07\quad m/sec$"

Answer 2

Answer:

velocity of wind = (5i-5j) m/s