a plane heads north but because of a wind blowing to the west the plane flies at a resultant velocity of 620mi/h 22 W of N .
what was the velocity of the wind?
To find the velocity of the wind, we can use vector addition.
Let's define the velocity of the plane as Vp (heading north) and the velocity of the wind as Vw (blowing west). The resultant velocity, Vr, is given as 620 mi/h, 22° W of N.
We can break down Vr into its north (Vr,N) and west (Vr,W) components using trigonometry:
Vr,N = Vr * sin(22°)
= 620 * sin(22°) ≈ 228.12 mi/h
Vr,W = Vr * cos(22°)
= 620 * cos(22°) ≈ 578.89 mi/h
Since the plane is heading north and the wind is blowing west, the northward velocity of the plane should be equal to the northward velocity of the resultant velocity:
Vp,N = Vr,N
= 228.12 mi/h
Now, we can find the westward velocity of the wind by subtracting the westward velocity of the resultant velocity from the westward velocity of the plane:
Vw,W = Vp,W - Vr,W
= 0 - 578.89 mi/h
= -578.89 mi/h
Therefore, the velocity of the wind is approximately 578.89 mi/h directed westward.
To find the velocity of the wind, we can use vector addition. The resultant velocity of the plane is 620 mi/h, 22° west of north. Let's break down this velocity into its north and west components.
The north component can be calculated by multiplying the magnitude of the velocity (620 mi/h) by the cosine of the angle (22°).
North component = 620 mi/h * cos(22°)
The west component can be calculated by multiplying the magnitude of the velocity (620 mi/h) by the sine of the angle (22°).
West component = 620 mi/h * sin(22°)
Now let's calculate the north and west components of the velocity:
North component = 620 mi/h * cos(22°) ≈ 572.1 mi/h
West component = 620 mi/h * sin(22°) ≈ 228.4 mi/h
The north component represents the actual velocity of the plane without any wind, while the west component represents the velocity caused by the wind.
Since the wind is blowing towards the west, the velocity of the wind is 228.4 mi/h to the west.
Therefore, the velocity of the wind is 228.4 mi/h west.