Question

A steamer is moving due east with
36 km/h. To a man in the steamer
the wind appears to blow at 18km/h
due north. The speed of the wind is
(A) 55 ms-1
(B) 5 ms-1
(C) 5V2 ms-1
-1
(D) 10 ms​

Answer 1

The speed of the wind is 5√5 m/s

Explanation:

If we take East as positive x-direction, North as positive y-direction

Then

The velocity of the steamer w.r.t. the Earth

$v_{S/E}=36\hat i$

And velocity of wind w.r.t. the steamer

$v_{W/S}=18\hat j$

Thus, velocity of wind w.r.t. the Earth

$v_{W/E}=v_{W/S}+v_{S/E}$

$\implies v_{W/E}=18\hat j+36\hat i$

$\implies v_{W/E}=36\hat i+18\hat j$

The magnitude of the velocity of the wind

$=\sqrt{36^2+18^2}$

$=\sqrt{18^2(2^2+1)}$

$=18\sqrt{5}$ km/h

$=18\sqrt{5}\times\frac{5}{18}$

$=5\sqrt{5}$ m/s

Hope this answer is helpful.

Know More:

Q: A person moves due east at a speed 6m/s and feels the wind is blowing towards south at a speed 6m/s.

(a) Find actual velocity of wind blow.

(b) If person doubles his velocity then find the relative velocity of wind blow w.r.t. man.​

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