Finding the direction and velocity of wind using vectors question

In summary, the question asks for the direction and velocity of the wind given a person traveling eastward at a rate of 4.0 km/hr. By drawing a vector triangle, the velocity of the wind relative to the person can be determined using the equation: Velocity of wind relative to person = Velocity of wind relative to the ground - velocity of person relative to the ground. The direction of the wind appears to be north, and its velocity can be calculated using the given information.
  • #1
shy9488
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Homework Statement



A person, traveling eastward at a rate of 4.0 km/hr, observes that the wind seems to blow directly from the north; on doubling his speed the wind appears to come from the northeast; determine the direction of the wind and its velocity.

Homework Equations





The Attempt at a Solution



My teacher has actually given us the answers on this question. However, I am stuck at the point where she says the
Velocity of wind relative to person = Velocity of wind relative to the ground - velocity of person relative to the ground.

I just can't understand this at all! Please help!
Thank you in advance!
 
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  • #2
welcome to pf!

hi shy9488! welcome to pf! :smile:
shy9488 said:
… I am stuck at the point where she says the
Velocity of wind relative to person = Velocity of wind relative to the ground - velocity of person relative to the ground.

I just can't understand this at all! Please help!

it means that if you draw the three vectors (with arrows), then they join up to form a vector triangle

(and when the question says "observes that the wind seems to blow directly from the north", it means that the velocity of the wind relative to the person is north)

see the pf library, or wikipedia, for details :wink:​
 

Related to Finding the direction and velocity of wind using vectors question

1. How do vectors help in finding the direction and velocity of wind?

Vectors are mathematical tools that can represent both the magnitude and direction of a physical quantity, such as wind velocity. By using vectors, we can break down the wind velocity into its components, one in the direction of the wind and one perpendicular to it. These components can then be used to determine the direction and speed of the wind.

2. What is the formula for calculating the direction and velocity of wind using vectors?

The formula for calculating the direction and velocity of wind using vectors is:

Wind Velocity = √(u² + v²)

Wind Direction = arctan(v/u)

Where u is the component of wind velocity in the direction of the wind, and v is the component perpendicular to the wind direction.

3. What units are used for measuring wind velocity and direction?

Wind velocity is typically measured in units of meters per second (m/s) or kilometers per hour (km/h). Wind direction is measured in degrees, with 0 degrees representing a wind blowing due north and 180 degrees representing a wind blowing due south.

4. Can vectors be used to calculate the wind direction and velocity at any location?

Yes, vectors can be used to calculate the wind direction and velocity at any location as long as the necessary data is available. This includes the wind velocity components, the location coordinates, and the necessary mathematical formulas.

5. Are there any limitations to using vectors to find the direction and velocity of wind?

While vectors can provide accurate calculations for wind direction and velocity, they may not always capture the full complexity of wind patterns. Meteorologists may also use other methods, such as numerical models, to better predict wind behavior and patterns.

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