# Relative Wind Problem (Modern Engineering Mathematics, 5th)

• SubZer0
In summary: So, in summary, a cyclist traveling east at a speed of 8 km/hr experiences wind blowing from the north. When the cyclist doubles their speed, the wind appears to blow from the north-east. By solving for the unknown variables using the given equations, it is determined that the actual velocity of the wind is 11.31 km/hr, with a magnitude of 11.31 km/hr.
SubZer0

## Homework Statement

A cyclist traveling east at 8 km/hr finds that the wind appears to blow directly from the north. On doubling his speed it appears to blow from the north-east.. Find the actual velocity of the wind.[/B]

## Homework Equations

Wind(relative) = Wind(Actual) - Velocity(cyclist)

## The Attempt at a Solution

I am completely stuck on this. I do know that there is a (16, 0) vector for the velocity of the cyclist, and a vector of -a(cos(45 deg), sin(45 deg)), which represents the relative, or perceived wind.

Slotting this into the relative wind equation,

Wind(r) = Wind(a) - Vel(cyclist)

-a*cos(45 deg) = Wx - 16
-a*sin(45 deg) = Wy

I'm not sure if this is even on the correct track.

Any trips highly appreciated.

SubZer0 said:
not sure if this is even on the correct track.
It is.
You just need to write the corresponding equations for the 8km/h case.

haruspex said:
It is.
You just need to write the corresponding equations for the 8km/h case.

Thanks heaps for the reply, haruspex. I think I just needed that little confidence boost you gave me to help solve the problem.

So now I have the full set of equations:

-a*cos(45 deg) + 16 = Wx
-a*sin(45 deg) = Wy
Wx = 8
Wy = b

Slotting Wx into the first equation;

8 = 16 - a*cos(45 degrees)
a = 11.3137

Slotting a into (2), gives:

Wy = -11.3137*sin(45 degrees)
Wy = -7.999 (approx 8)

Therefore, actual wind velocity has vector of (8, -8). Magnitude, of sqrt(64+64) = 11.31km/hr

Thanks, haruspex!

SubZer0 said:
actual wind velocity has vector of (8, -8).
Looks right.

## 1. What is the relative wind problem?

The relative wind problem is a mathematical concept used in engineering to determine the forces acting on a body in motion, taking into account the velocity and direction of the air or wind relative to the body.

## 2. Why is the relative wind problem important in engineering?

The relative wind problem is important because it helps engineers understand the aerodynamic forces acting on structures and vehicles in motion, such as airplanes, cars, and wind turbines. This information is crucial for designing and optimizing these structures for efficiency and safety.

## 3. How is the relative wind problem solved?

The relative wind problem is solved using vector algebra and trigonometry. By breaking down the velocity of the air and the velocity of the body into their individual components, engineers can determine the relative velocity and direction of the wind, and then calculate the forces acting on the body.

## 4. What are some real-world applications of the relative wind problem?

The relative wind problem is used in a variety of real-world applications, such as designing aircraft and spacecraft, analyzing the aerodynamics of cars and other vehicles, and optimizing the placement and orientation of wind turbines for maximum energy production.

## 5. Are there any limitations to the relative wind problem?

While the relative wind problem is a useful tool in engineering, it does have some limitations. It assumes that the air is moving in a uniform and steady manner, which may not always be the case in real-world situations. It also does not take into account other factors such as turbulence and air density, which can have an impact on the forces acting on a body in motion.

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