Question

a streamer is sailing directly south at 25 km/h in an area, where the wind is due the south - west at 18 km/hr. what is the angle from true north of the smoke trail from the stack?​

Answer 1

The angle from true north of the smoke trail from the stack is 18.65°

Explanation:

Taking the East direction as +x direction and North as +y direction

The velocity of the streamer

$v_s=-25\hat j$

Velocity of the wind

$v_w=-18\cos 45^\circ\hat i-18\sin\45^\circ\hat j$

$\implies v_w=-\frac{18}{\sqrt{2}}(\hat i+\hat j)$

The resultant velocity will be

$v_{R}=v_s-v_w$

$\implies v_{R}=-25\hat j+[-\frac{18}{\sqrt{2}}(\hat i+\hat j)]$

$\implies v_{R}=-\frac{18}{\sqrt{2}}\hat i-(\frac{18}{\sqrt{2}}+25)\hat j$

The angle that the streamer makes with West (-x axis)

$\theta=\tan^{-1}(\frac{18/\sqrt{2}+25}{18/\sqrt{2}})$

$\implies \theta=\tan^{-1}\frac{18+25\sqrt{2}}{18}$

$\implies \theta=\tan^{-1}(2.96)$

$\implies \theta=71.35^\circ$

The angle that the smoke of the streamer makes with East will be just opposite to it.

Therefore, the angle that the smoke makes with east will also be $1.35^\circ$ due to opposite angles

Thus, the angle that the smoke makes with the north

$=90^\circ-71.35^\circ$

$=18.65^\circ$

Hope this answer is helpful.

Know More:

Q: A ship is moving towards N-E with a velocity of  10 km/hr and to a passenger on board the wind  appears to blow from the north with a velocity of  10√2 km/hr. Actual velocity of the wind is​ :

Click Here: https://brainly.in/question/11752233

Answer 2

Answer:

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