# Relative Velocity, Aeroplane Problem

• TheRedDevil18
We know that the plane is flying due west at a speed of 225km/h and the distance traveled is 119km west and 14km south. This gives us the following equation:225km/h = \vec{V}_{plane/air} + \vec{V}_{air/ground}Using Pythagoras' Theorem, we can find the magnitude of the wind velocity:|\vec{V}_{air/ground}| = \sqrt{(119km)^2 + (14km)^2} = 120kmSubstituting this into our equation, we get:225km/h = \vec{V}_{plane/air} + 120km/hSolving for \vec{V}_{plane/
TheRedDevil18

## Homework Statement

An airplane pilot sets a compass course due west and maintains an airspeed of 225km/h . After flying for a time of 0.470h , she finds herself over a town a distance 119km west and a distance 14km south of her starting point.

1) Find the magnitude of the wind velocity.

2) Find the direction of the wind velocity.

3) If the wind velocity is 36km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 225km/h

## The Attempt at a Solution

I'm stuck at the first one

This is what I tried,

sqrt(119^2 + 14^2) = 120km

120/0.47 = 255km/h

Wind speed = sqrt(255^2 - 225^2)
= 120km/h, which is incorrect, any help ?

Set up a vector equation:
$$\vec{V}_{plane/ground} = \vec{V}_{plane/air} + \vec{V}_{air/ground}$$

## 1. What is relative velocity?

Relative velocity refers to the velocity of an object in relation to another object. It takes into account the motion of both objects and can be calculated by subtracting the velocity of one object from the velocity of the other.

## 2. How is relative velocity used in aeroplane problems?

In aeroplane problems, relative velocity is used to calculate the speed and direction of the plane in relation to the ground or other objects. It takes into account the speed and direction of the plane, as well as any winds or currents that may affect its motion.

## 3. What is the difference between airspeed and groundspeed?

Airspeed is the speed of an aircraft in relation to the air around it, while groundspeed is the speed of the aircraft in relation to the ground. Groundspeed takes into account the effects of wind and other external factors, while airspeed does not.

## 4. How does the angle of wind affect relative velocity in aeroplane problems?

The angle of wind can affect the direction and speed of relative velocity in aeroplane problems. For example, a headwind (wind blowing in the opposite direction of the plane's motion) can decrease the groundspeed of the plane, while a tailwind (wind blowing in the same direction as the plane's motion) can increase the groundspeed.

## 5. How can relative velocity be calculated in aeroplane problems?

Relative velocity can be calculated using vector addition and subtraction. This involves breaking down the velocity vectors of the plane and other objects into their horizontal and vertical components, and then adding or subtracting the components to find the resultant velocity. Alternatively, the Pythagorean theorem can be used to calculate the magnitude and direction of the resultant velocity.

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