To find the relative velocity of the wind as seen from a car

In summary, the conversation is about finding the true velocity of wind relative to a moving car in different situations. The equations for the wind's velocity are given for two different cases, and the third case involves solving for the velocity when the motorist is heading north. The conversation ends with the realization of a mistake in the equations and the confirmation that the method works.
  • #1
gnits
137
46
Homework Statement
To find the relative velocity of the wind as seen from a car
Relevant Equations
Vab=Va-Vb
Could I please ask for any help with the following question:

Capture.PNG


Here's my attempt: (i and j are unit vectors in the directions of east and north respectively)

(apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram)

wind.png


Let the velocity of the wind relative to the car be V_wc then:

V_wc = V_w - V_c

therefore V_w = V_wc + V_c

This is the true velocity of the wind.

In the first situation call the apparent magnitude of the wind's velocity K1 and in the second call it K2 then:

Case 1: V_w = -K1 * cos(T) i + ( K1 * sin(T) - u ) j

Case 2: V_w = -K2 * cos(P) i + ( K2 * sin(P) + u ) j

Now I can eliminate K1 and solve for K2, I get:

K2 = 2u / ( cos(P) tan(T) - sin(P) )

I can substitute this into the Case 2 equation for V_w to obtain:

V_w = ( -2u / [ tan(T) - tan(P) ] ) i + ( 2u / [ tan(T) tan(P) - 1 ] + u ) j

So this is the true velocity of the wind.

So now, for case 3 where the speed of the motorist is 2u heading north I need to find:

V_wc = V_w - V_c = ( -2u / [ tan(T) - tan(P) ] ) i + ( 2u / [ tan(T) tan(P) - 1 ] - u ) j

This leads to :

2 tan(w) = ( ( 2 / [ tan(T) tan(P) - 1 ] - 1 ) ) * (tan(T) - tan(P))

Which is not the desired answer.

Thanks for any help,
Mitch.
 
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  • #2
Just finished writing and posting this, then after all that effort, I found my mistake - an algebraic slip. The method works.
 

Related to To find the relative velocity of the wind as seen from a car

1. How do you calculate relative velocity of wind from a moving car?

The relative velocity of wind from a moving car can be calculated by subtracting the velocity of the car from the velocity of the wind. This can be represented by the equation Vrel = Vwind - Vcar, where Vrel is the relative velocity, Vwind is the velocity of the wind, and Vcar is the velocity of the car.

2. What factors affect the relative velocity of wind as seen from a car?

The relative velocity of wind as seen from a car can be affected by the speed of the car, the direction of the wind, and the angle at which the wind is hitting the car. Other factors such as the shape and size of the car can also influence the relative velocity.

3. Can the relative velocity of wind from a car be negative?

Yes, the relative velocity of wind from a car can be negative. This occurs when the wind is blowing in the opposite direction of the car's motion. In this case, the relative velocity would be a negative value, indicating that the wind is slowing down the car.

4. How does the relative velocity of wind from a car affect fuel efficiency?

The relative velocity of wind from a car can have a significant impact on fuel efficiency. When the wind is blowing in the same direction as the car's motion, it can reduce the air resistance and improve fuel efficiency. However, if the wind is blowing in the opposite direction, it can increase air resistance and decrease fuel efficiency.

5. Can the relative velocity of wind from a car be greater than the speed of the car?

Yes, the relative velocity of wind from a car can be greater than the speed of the car. This can occur when the wind is blowing in the same direction as the car's motion and has a higher velocity than the car. In this case, the relative velocity would be a positive value, indicating that the wind is helping to increase the car's speed.

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