Proof of known velocity of wind

In summary, the conversation discussed a theoretical approach to calculating the velocity of wind relative to a person moving northeast. However, it was noted that in reality, the person's velocity and wind patterns may vary, and other factors such as air pressure and temperature should also be considered. It was concluded that while the solution provided a theoretical understanding, it may not accurately reflect real-world conditions.
  • #1
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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.
 
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  • #2

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.
 

1. How is the velocity of wind measured?

The velocity of wind is typically measured using an anemometer, which is a device that rotates in response to the wind and records the number of rotations per unit time. This data can then be used to calculate the wind speed in miles per hour or meters per second.

2. What factors can affect the accuracy of wind velocity measurements?

There are several factors that can affect the accuracy of wind velocity measurements, including the height at which the anemometer is placed, the type of anemometer used, and any obstructions or changes in terrain that may influence the wind flow.

3. How do scientists use wind velocity data?

Scientists use wind velocity data to study weather patterns, climate change, and the effects of wind on the environment. This data can also be used to predict wind speeds and patterns, which is important for industries such as aviation and renewable energy.

4. How can the known velocity of wind be used to improve building design?

The known velocity of wind is an important factor in building design, as it can help engineers determine the structural integrity and stability of a building. By incorporating wind velocity data into building design, structures can be built to withstand high winds and reduce the risk of damage or collapse.

5. Can wind velocity data be used to predict severe weather events?

Yes, wind velocity data can be used to predict severe weather events such as hurricanes, tornadoes, and thunderstorms. By analyzing wind patterns and speeds, scientists can identify potential areas for severe weather and issue warnings to help keep people and property safe.

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