Proof of known velocity of wind

[WMDhamnekar]

My attempt to answer this question: Let the actual velocity of wind is $\vec{v}=x\hat{i} + y\hat{j}$ where $\hat{i}$ and $\hat{j} $ represents velocities of 1KM per hour towards east and north respectively. As the person is going northeast with a velocity of 6KM/hr, his actual velocity is $ 3\sqrt{2} \hat{i} +3\sqrt{2}\hat{j}$

Then the velocity of wind relative to person is $x\hat{i} -y\hat{j}- 3\sqrt{2}\hat{i} -3\sqrt{2}\hat{j}$ which is parallel to $-3\sqrt{2}\hat{j}$ as it appears to blow from the north. Hence $x=3\sqrt{2},y=(3\sqrt{2}-k)\hat{j}$

When the velocity of the person becomes $6\sqrt{2}\hat{i} + 6\sqrt{2}\hat{j} $, the velocity of the wind relative to person is $(3\sqrt{2}\hat{i}+(3\sqrt{2}-k)\hat{j}) - 6\sqrt{2}\hat{i} -6\sqrt{2}\hat{j} $ So velocity of wind relative to person is $-3\sqrt{2}\hat{i}+(-3\sqrt{2}-k)\hat{j}$

$\frac{-3\sqrt{2}-k}{-3\sqrt{2}}=2 \rightarrow k=3\sqrt{2}$, Hence velocity of wind is $3\sqrt{2}\hat{i} +(3\sqrt{2}-3\sqrt{2})\hat{j}$.

Thus we showed that actual velocity of wind is $3\sqrt{2}$ KM/hr towards east.

 

[jvicens]

Thank you for sharing your attempt to answer the question about the velocity of wind relative to a person moving northeast. I would like to offer some insights on your solution.

Firstly, your calculations seem to assume that the person's velocity is constant at 6KM/hr. However, in reality, the person's velocity may vary as they move northeast. Therefore, the velocity of wind relative to the person may also vary.

Additionally, your solution assumes that the wind is blowing in a straight line towards the northeast. In reality, wind patterns can be more complex and may not always follow a straight path. Therefore, the actual velocity of the wind may not be exactly $3\sqrt{2}$ KM/hr towards east.

Furthermore, it is important to consider the effects of other factors such as air pressure, temperature, and terrain on wind velocity. These factors can greatly influence the direction and speed of wind, and may not always align with the person's velocity.

In conclusion, while your solution provides a theoretical approach to calculating the velocity of wind relative to a person moving northeast, it may not accurately reflect the actual conditions in a real-world scenario. As scientists, we must always consider various factors and gather empirical data to make informed conclusions. Thank you for your contribution to the discussion.