Another pilot flies her plane at 300.0 km/h at 20.0° north of east. If the wind blows at 50.0 km/h at 45.0° northwest, what is the plane’s displacement from its starting point?
with procedure please!
To find the plane's displacement from its starting point, we can break down the given information into its components and then apply vector addition.
Let's start by finding the eastward and northward components of the plane's velocity.
The eastward component is calculated by multiplying the plane's speed (300.0 km/h) by the cosine of the angle north of east (20.0°).
Eastward component = 300.0 km/h * cos(20.0°)
The northward component is calculated by multiplying the plane's speed (300.0 km/h) by the sine of the angle north of east (20.0°).
Northward component = 300.0 km/h * sin(20.0°)
Next, we need to find the eastward and northward components of the wind velocity.
The eastward component is calculated by multiplying the wind's speed (50.0 km/h) by the cosine of the angle northwest (45.0°).
Eastward component = 50.0 km/h * cos(45.0°)
The northward component is calculated by multiplying the wind's speed (50.0 km/h) by the sine of the angle northwest (45.0°).
Northward component = 50.0 km/h * sin(45.0°)
Now, we add together the eastward components of the plane's velocity and the wind's velocity.
Total eastward component = Eastward component of the plane + Eastward component of the wind
Similarly, we add together the northward components of the plane's velocity and the wind's velocity.
Total northward component = Northward component of the plane + Northward component of the wind
Given the total eastward and northward components, we can use the Pythagorean theorem to find the magnitude of the plane's displacement.
Magnitude of displacement = √[ (Total eastward component)^2 + (Total northward component)^2 ]
Finally, the direction of the displacement can be determined by finding its angle relative to the eastward direction. This can be calculated using the inverse tangent function:
Direction = arctan( Total northward component / Total eastward component )
By following these steps and plugging in the given values, you can find the plane's displacement from its starting point.