Find the magnitude and relative direction (e.g., NE, NW, SE, SW) of the velocity of an airplane relative to the earth, if the velocity of the airplane relative to the air is 165 km/hr. south to north and the wind velocity is 65 km/hr. at an 50o angle from east to west.
To find the magnitude and relative direction of the velocity of the airplane relative to the earth, we need to consider the vector addition of the velocity of the airplane relative to the air and the wind velocity.
1. Convert the given velocities into vector form:
- Velocity of the airplane relative to the air: 165 km/hr north
- Wind velocity: 65 km/hr at a 50° angle from east to west
The vector form of the velocity of the airplane relative to the air is (0 km/hr, 165 km/hr), and the vector form of the wind velocity is (65 * cos(50°) km/hr, -65 * sin(50°) km/hr).
2. Use vector addition to find the velocity of the airplane relative to the earth:
Add the two vectors together:
Velocity of the airplane relative to the earth = Velocity of the airplane relative to the air + Wind velocity
(0 km/hr, 165 km/hr) + (65 * cos(50°) km/hr, -65 * sin(50°) km/hr)
The resulting vector is the velocity of the airplane relative to the earth.
3. Calculate the magnitude of the velocity of the airplane relative to the earth:
Use the Pythagorean theorem:
Magnitude = √[(horizontal component)^2 + (vertical component)^2]
Magnitude = √[(0 km/hr + 65 * cos(50°) km/hr)^2 + (165 km/hr - 65 * sin(50°) km/hr)^2]
Calculate the value.
4. Determine the relative direction of the velocity of the airplane relative to the earth:
Use trigonometry to find the relative direction.
Direction = atan2(vertical component, horizontal component)
Calculate the direction.
After following these steps, you will have the magnitude and relative direction of the velocity of the airplane relative to the earth.
To find the magnitude and relative direction of the velocity of an airplane relative to the earth, we need to consider the effect of the wind on the airplane's motion.
Let's break down the given information:
1. Velocity of the airplane relative to the air = 165 km/hr, south to north.
2. Wind velocity = 65 km/hr, at a 50° angle from east to west.
To find the magnitude and direction of the velocity of the airplane relative to the earth, we can use vector addition. We need to add the velocity of the airplane relative to the air and the velocity of the wind.
1. Convert the given velocities to vectors:
Velocity of airplane relative to air: 165 km/hr, south to north
This can be represented as a vector: 165 km/hr, north (-y direction)
Velocity of wind: 65 km/hr, at a 50° angle from east to west
We can break down this vector into its x and y components using trigonometry:
x-component = 65 km/hr * cos(50°)
y-component = 65 km/hr * sin(50°)
2. Add the vectors:
To add the vectors, add the x-components and the y-components separately.
x-component of velocity = x-component of airplane velocity + x-component of wind velocity
y-component of velocity = y-component of airplane velocity + y-component of wind velocity
3. Calculate the magnitude:
Magnitude of velocity = √(x-component of velocity)^2 + (y-component of velocity)^2
4. Calculate the direction:
To determine the relative direction of the velocity, we can use trigonometry.
Direction of velocity = tan^(-1) (y-component of velocity / x-component of velocity)
Once you perform these calculations, you will have the magnitude and relative direction of the velocity of the airplane relative to the earth.