A plane travels at 300km/h relative to the ground in direction 300 degrees from east. A wind of 84km/h blows in direction of 225 degree from east. What is velocity of plane relative to air
To find the velocity of the plane relative to the air, we need to use vector addition. Let's break down the given information:
Plane's velocity relative to the ground:
- Magnitude: 300 km/h
- Direction: 300 degrees from east
Wind velocity:
- Magnitude: 84 km/h
- Direction: 225 degrees from east
To find the velocity of the plane relative to the air, we need to subtract the wind velocity from the plane's velocity relative to the ground.
To subtract these vectors, we can break them down into their horizontal and vertical components.
Plane's velocity relative to the ground:
- Horizontal component: 300 km/h * cos(300 degrees)
- Vertical component: 300 km/h * sin(300 degrees)
Wind velocity:
- Horizontal component: 84 km/h * cos(225 degrees)
- Vertical component: 84 km/h * sin(225 degrees)
Now, we can subtract the horizontal and vertical components separately:
Horizontal component of plane's velocity relative to air:
= Horizontal component of plane's velocity relative to the ground - Horizontal component of wind velocity
= 300 km/h * cos(300 degrees) - 84 km/h * cos(225 degrees)
Vertical component of plane's velocity relative to air:
= Vertical component of plane's velocity relative to the ground - Vertical component of wind velocity
= 300 km/h * sin(300 degrees) - 84 km/h * sin(225 degrees)
Finally, we can use these components to find the magnitude and direction of the velocity of the plane relative to the air using the Pythagorean theorem and trigonometry:
Magnitude of plane's velocity relative to air:
= sqrt((horizontal component of plane's velocity relative to air)^2 + (vertical component of plane's velocity relative to air)^2)
Direction of plane's velocity relative to air:
= arctan(vertical component of plane's velocity relative to air / horizontal component of plane's velocity relative to air)
Calculating these values gives us the velocity of the plane relative to the air.