# Vector equation help: Find Wind Velocity Vector

• Zanesco
In summary: So the plane is heading at a speed of 426.77 km/h due north and at a speed of 172.41 km/h due east. The pilot wants to fly 784 km directly north, so the total distance traveled in the direction the pilot wants to go is 784 km. If the total travel time is 2.07 hrs, then the magnitude of the wind velocity vector can be found using the formula v=d/t. So v=784 km/2.07 hrs= 378.5 km/h. Therefore, in summary, the magnitude of the wind velocity vector is 378.5 km/h.
Zanesco

## Homework Statement

An airplane flies at an airspeed of 459 km/hr. The pilot wants to fly 784 km to the north. She knows that she must head 21.6° east of north to fly directly there. If the plane arrives in 2.07 hr, find the magnitude of the wind velocity vector.

Tried solving as seen below but I'm not sure where I'm going wrong.

## The Attempt at a Solution

v=d/t
459 km/h=d/2.07 h
950.13 km=d

srt(950.13^2-784^2)=b
66.05 km=b

v=66.05 km/2.07 h
v=31.9 km/h

Last edited:

Zanesco said:

## Homework Statement

An airplane flies at an airspeed of 459 km/hr. The pilot wants to fly 784 km to the north. She knows that she must head 21.6° east of north to fly directly there. If the plane arrives in 2.07 hr, find the magnitude of the wind velocity vector.

Tried solving as seen below but I'm not sure where I'm going wrong.

## The Attempt at a Solution

v=d/t
459 km/h=d/2.07 h
950.13 km=d

srt(950.13^2-784^2)=b
66.05 km=b

v=66.05 km/2.07 h
v=31.9 km/h
The plane flies in the air at a speed of 459 km/h for 2.07 hrs, so the distance is correct. However, the plane flies at an angle of 21.6 deg E of N. What is the projection from the planes trajectory in the air on to due north?

it would be: 459cos21.6=426.77 km/h

## 1. What is a vector equation?

A vector equation is a mathematical representation of a vector, which is a quantity that has both magnitude (size) and direction. It is typically written in the form of a + b = c, where a and b are vectors and c is the resulting vector when they are added together.

## 2. How do you find the wind velocity vector?

To find the wind velocity vector, you need to know the speed and direction of the wind. This information can be obtained from a weather station or by using an anemometer, which measures wind speed. Once you have these values, you can use trigonometry to calculate the x and y components of the vector, which can then be combined to form the wind velocity vector.

## 3. What is the difference between speed and velocity?

Speed is a scalar quantity that refers to the rate at which an object is moving, while velocity is a vector quantity that also takes into account the direction of motion. So while speed tells you how fast something is going, velocity tells you both how fast and in what direction.

## 4. How is wind velocity vector used in science?

The wind velocity vector is used in many scientific fields, including meteorology, climatology, and fluid dynamics. It is used to model and predict weather patterns, study air and water currents, and understand the movement of gases and liquids in various environments.

## 5. What are some real-life applications of wind velocity vector?

The wind velocity vector has many practical applications, such as in aviation and sailing, where it is used to determine the best routes and to make adjustments for wind resistance. It is also used in architecture and engineering to design buildings and structures that can withstand high winds. Additionally, the wind velocity vector is important in the field of renewable energy, as it helps determine the best locations for wind turbines to generate electricity.

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