Calculating wind speed with respect to an airplane

[kvandeaver]

Homework Statement

An airplane pilot sets a compass course due west and maintains an airspeed of 220 km/hr. After flying for .5 hr, she finds herself over a town 120 km west and 20 km south of her starting point. Find the wind velocity (magnitude and direction).

Homework Equations

The Attempt at a Solution

I have attempted setting up the diagram and finding the vector components of each velocity, and then using right triangles to find the magnitudes, but I keep getting the wrong answer. I have no idea how to go about doing this problem.

 

[KLoux]

Can you show us how you set up your vector equations?

-Kerry

 

[nlightner]

I would suggest starting by breaking down the given information into smaller, more manageable components. First, we know that the airplane's airspeed is 220 km/hr and it has flown for 0.5 hours. This means that the airplane has traveled a distance of 110 km (220 km/hr x 0.5 hr).

Next, we can create a diagram to represent the situation. The airplane's starting point can be represented as point A, and the town it is currently over can be represented as point B. The distance between A and B is 120 km west and 20 km south, which can be represented as a displacement vector.

Using the given information, we can also calculate the airplane's velocity vector (vA) by dividing the distance traveled (110 km) by the time (0.5 hr). This gives us a velocity of 220 km/hr due west.

Now, we can use the displacement vector and the velocity vector to find the wind velocity vector (vW). By using vector addition, we can find the resultant vector, which represents the wind velocity. We can then use trigonometry to find the magnitude and direction of the wind velocity.

In summary, to find the wind velocity with respect to the airplane, we need to use vector addition and trigonometry to find the resultant vector of the displacement vector and the airplane's velocity vector. This will give us the magnitude and direction of the wind velocity.