# Vectors - Aircraft's velocity relative to ground

• g9WfI
In summary, the conversation discusses a problem with calculating ground speed and airspeed on a windy day. The individual is unsure about the highlighted equation and how to change their vector diagram. They are also seeking help in understanding how to solve this type of problem and how to correctly draw vector diagrams.
g9WfI
Homework Statement
An aircraft is scheduled to fly from London to Belfast, a distance of 510 km in a direction N 40 W. The aircraft has a cruising speed of 240 m/s in still air. On the day of the flight, there is a wind of velocity 15 m/s towards the east. Find the direction in which the aircraft must fly to reach Belfast without any change of course, and the magnitude of the velocity of the aircraft relative to the ground.
Relevant Equations
relative velocities, cosine rule, sine rule
I attach my working below - my angle is correct according to mark scheme but magnitude isn't (should be 230).
I think it's odd that my resultant velocity on a windy day is larger than velocity in still air, but apparently my angle is correct?

I've been told that I've calculated the airspeed it would need if it were to maintain a ground speed of 240 m/s... And the question asked for the ground speed given that the airspeed is 240.

I don't fully understand the above statement. Is the highlighted equation in my working correct? How do I change my vector diagram? At the moment, I can't see any other way to use the information given.

It appears I just don't know how to do this q - I haven't seen an example like this before. I'd be so grateful for any help.

You have two vectors emanating from the same point, then draw the resultant as connecting their endpoints.
Instead, you can use either of the following:
1. Nose to tail: Draw one vector from point O to point A, and the second vector from A to B. The resultant is then OB.
2. Complete the parallelogram: Draw one vector from O to A and the second from O to B. Now draw AC and BC so that OACB is a parallelogram. The resultant is OC.

It will help if you draw the magnitude 240 vector longer than the magnitude 15 vector!

## 1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size or length) and direction. It is represented by an arrow pointing in the direction of the vector with the length of the arrow representing the magnitude.

## 2. How is an aircraft's velocity relative to the ground represented as a vector?

An aircraft's velocity relative to the ground is represented as a vector by using the aircraft's airspeed (magnitude) and heading (direction). The vector is drawn from the origin (starting point) to the endpoint, which represents the aircraft's position after a certain amount of time has passed.

## 3. What factors affect an aircraft's velocity relative to the ground?

An aircraft's velocity relative to the ground is affected by its airspeed, heading, wind speed and direction, and the Earth's rotation. These factors can either increase or decrease the aircraft's velocity relative to the ground.

## 4. How is the aircraft's velocity relative to the ground calculated?

The aircraft's velocity relative to the ground can be calculated by using vector addition. The aircraft's airspeed and heading are added to the wind velocity (which is represented as a vector in the opposite direction) to get the aircraft's velocity relative to the ground.

## 5. Why is it important for pilots to understand vectors and an aircraft's velocity relative to the ground?

Understanding vectors and an aircraft's velocity relative to the ground is crucial for pilots to accurately navigate and control their aircraft. It allows them to make necessary adjustments based on wind conditions and maintain safe airspeed and heading to reach their destination. It also helps in avoiding collisions with other aircraft and obstacles on the ground.

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