Velocity is Relative: Reference Frames

[DeaZ]

1. The Question Verbatim
"A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0 N of E (LETS CALL THIS VECTOR = A). The pilot heads directly for Sparta and flies at an airspeed of 160km/h. After flying 2.0 h, the pilot expects to be at Sparta but instead he finds himself 20 km due west of Sparta (LETS CALL THIS VECTOR= B) He has forgotten to correct for the wind.

1) What is the velocity of the plane relative to the air?
2) Find the velocity (magnitude and direction) of the plane relative to the ground
3) Find the wind speed and direction.
2. The attempt at a solution

-The vector connecting the origin to vector B will be called Vector C. My first problem is finding the proper angle. I know that vector A is 20deg north of east ... but I don't know how to find the angle, at the origin, for the triangle. It isn't a right-angle, and the 20deg applies to a much larger area.

The second issue I have is distinguishing what is what. From what I understand, the velocity of the plane relative to the air (question 1) is vector C. The velocity of the plane relative to the ground ... to me ... also seem to be vector C. Am I missing something here?

 

[learningphysics]

You should be able to use right triangles to find the new angle...

Draw a picture of the origin, Sparta... the line joining the origin and sparta is 320Km... it forms an angle of 20 degrees with the east axis... so you have a right triangle... hypoteneuse 320, angle 20.

But the plane ends up 20km west of sparta... draw that point... draw a line joining the origin and that point... you can draw a new right triangle... the new right triangle has the same height as the previous... but the base is 20km less... you should be able to find the new angle...

 

[m2003]

I would like to clarify the concept of relative velocity and reference frames in this scenario. Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It has both magnitude and direction, and it is always measured in relation to a reference frame.

In this scenario, we have two reference frames - the air and the ground. The pilot's airspeed of 160 km/h is the velocity of the plane relative to the air. This means that the plane is moving at 160 km/h with respect to the air around it. However, because the air itself is moving due to the wind, the plane's velocity relative to the ground will be different.

To find the velocity of the plane relative to the ground, we need to consider the vector addition of the plane's velocity relative to the air (vector C) and the wind's velocity (vector D). This can be done using the Pythagorean theorem and trigonometric functions. The result will be a new vector, which we can call vector E. The magnitude of vector E will give us the velocity of the plane relative to the ground, and its direction will give us the direction in which the plane is moving with respect to the ground.

Now, the wind's velocity can be calculated by subtracting vector C from vector E. This will give us the wind's velocity relative to the ground, which is 20 km/h in the west direction. The wind's direction can be found by using trigonometric functions on vector D.

In conclusion, velocity is always relative to a reference frame, and in this scenario, we have two reference frames - the air and the ground. The pilot's airspeed is the velocity of the plane relative to the air, and the velocity of the plane relative to the ground is a combination of the plane's airspeed and the wind's velocity. It is important to consider the concept of relative velocity and reference frames when solving problems involving motion.