Vector problem involving velocity and wind

In summary, the 100-meter dash is run in the direction of 2\vec{e_{1}}+6\vec{e_{2}} and the wind velocity is 5\vec{e}_{1}+\vec{e_{2}} km/h. According to the rules, the wind speed measured in the direction of the race must not exceed 5 km/h. This means that the race results will not be disqualified due to an illegal wind.
  • #1
braindead101
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A 100-meter dash is run on a track in the direction of [tex]\vec{v} = 2\vec{e_{1}}+6\vec{e_{2}}[/tex]. The wind velocity [tex]\vec{w}[/tex] is 5[tex]\vec{e}_{1}+\vec{e_{2}}[/tex] km/h. The rules say that a legal wind speed measured in teh direction of the dash must not exceed 5 km/h. Will the race results be disqualified due to an illegal wind?

I am unsure how to start this problem, any help would be great. I think that I must find the speed of the wind in that direction first, so finding that vector and then finding the magnitude of that vector. But I don't know how to find that vector.
 
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  • #2
If the wind speed is 5 km/h in any given direction, then it has to be less in a particular direction. So it cannot exceed 5 km/h in the track's direction.
 

1. How does wind affect the velocity of an object?

Wind can either increase or decrease the velocity of an object, depending on the direction and strength of the wind. If the wind is blowing in the same direction as the object's motion, it will add to the object's velocity, making it move faster. If the wind is blowing in the opposite direction, it will decrease the object's velocity, making it move slower.

2. How do you calculate the resultant velocity in a vector problem involving wind?

To calculate the resultant velocity, you need to use vector addition. This involves finding the vector components of the object's velocity and the wind's velocity, and then adding them together using the Pythagorean theorem. This will give you the magnitude and direction of the resultant velocity.

3. How does the angle of the wind impact the velocity of an object?

The angle of the wind can have a significant impact on the velocity of an object. If the wind is blowing directly against the object's motion (headwind), it will decrease the velocity. If the wind is blowing in the same direction as the object's motion (tailwind), it will increase the velocity. If the wind is blowing at an angle, it will have a combined effect on the object's velocity.

4. Can you use vector diagrams to solve problems involving velocity and wind?

Yes, vector diagrams are a useful tool for solving problems involving velocity and wind. They allow you to visualize the vectors involved and determine the direction and magnitude of the resultant velocity. By drawing the vectors to scale, you can accurately calculate the resultant velocity using vector addition.

5. How can you determine the direction of the resultant velocity in a vector problem involving wind?

The direction of the resultant velocity can be determined by using trigonometry. You can use the tangent ratio to find the angle of the resultant velocity, which is the direction that the object will move. Alternatively, you can use the inverse tangent function to find the direction of the resultant velocity, given the magnitudes of the vector components.

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