Showing Plane's Relation to Earth w/ Two Vectors

[Max CR]

Homework Statement

How can i show the relationship of a plane relative to the Earth using two given vectors?
The nose of an ultralight plane is pointed south, and its airspeed indicator shows 35 m/s. The plane is in a 10 m/s wind blowing toward the southwet relative to the earth.

a) In a vector addition diagram, show the relationship of the vector of the velocity of the plane relative to the Earth to the two given vectors.

b) Leting x be east and y be north, find the components of the vector of plane relative to the earth.

c) Find the magnitude and direction of the vector of the plane relative to the earth

Homework Equations

The Attempt at a Solution

I am unsure how to start this problem. I have tried using a freebody diagram but that wasnt useful.

 

[rl.bhat]

Show your attempts.

 

[tomcue]

I would suggest approaching this problem by breaking down the given information into smaller, more manageable pieces. Let's start with the given vectors: the plane's velocity and the wind's velocity. We can represent these as vectors in a coordinate system, with the x-axis pointing east and the y-axis pointing north.

a) To show the relationship between the plane's velocity relative to the Earth and the given vectors, we can use vector addition. Start by drawing the plane's velocity vector, pointing south with a magnitude of 35 m/s. Then, draw the wind's velocity vector, pointing towards the southwest with a magnitude of 10 m/s. The vector representing the plane's velocity relative to the Earth can be found by adding these two vectors together. This new vector will have a magnitude and direction that represents the overall velocity of the plane relative to the Earth.

b) To find the components of the plane's velocity relative to the Earth, we can use trigonometry. We know that the plane's velocity has a magnitude of 35 m/s and is pointing south, so its y-component (north-south direction) is 35 m/s and its x-component (east-west direction) is 0 m/s. For the wind's velocity, we can use the given direction and magnitude to find its x and y components using trigonometry. Once we have these components, we can add them together to find the components of the overall velocity vector of the plane relative to the Earth.

c) To find the magnitude and direction of the overall velocity vector, we can use the Pythagorean theorem and trigonometry. The magnitude of the vector can be found by taking the square root of the sum of the squares of the x and y components. The direction can be found by using inverse trigonometric functions to find the angle between the vector and the positive x-axis.

In summary, to show the relationship between the plane's velocity relative to the Earth and the given vectors, we can use vector addition. To find the components of the plane's velocity relative to the Earth, we can use trigonometry. And to find the magnitude and direction of the overall velocity vector, we can use the Pythagorean theorem and trigonometry.