A plane is steering east at a speed of 240km/h. What is the ground speed of the plane if the wind is from the northwest at 65km/h. What is the plane's actual direction?
I answered this for you at 10:00 this morning.
I even gave you two different methods, both yielding the same answer.
Why are you reposting it?
To determine the ground speed of the plane, we need to calculate the resultant velocity vector by taking into account the velocity of the plane and the velocity of the wind.
The plane is steering east at a speed of 240 km/h. This means that its velocity vector is pointing due east with a magnitude of 240 km/h.
The wind is coming from the northwest, which is 45 degrees north of west. The wind has a speed of 65 km/h. To find the velocity vector of the wind, we can decompose it into its north and west components.
The west component of the wind is calculated by multiplying the wind speed by the cosine of the angle between the wind direction and due west (45 degrees). So the west component of the wind is 65 km/h * cos(45) ≈ 46.1 km/h.
The north component of the wind is calculated by multiplying the wind speed by the sine of the angle between the wind direction and due west (45 degrees). So the north component of the wind is 65 km/h * sin(45) ≈ 46.1 km/h.
Now we can add the eastward velocity of the plane (240 km/h) and the westward component of the wind (46.1 km/h) to find the resultant eastward velocity:
240 km/h + 46.1 km/h = 286.1 km/h
Next, we can subtract the northward component of the wind (46.1 km/h) from the resultant eastward velocity to find the ground speed:
286.1 km/h - 46.1 km/h = 240 km/h
So the ground speed of the plane is 240 km/h.
To find the plane's actual direction, we can use trigonometry. The actual direction of the plane is given by the angle between the resultant velocity vector and due east.
To find this angle, we can use the inverse tangent function:
angle = arctan(north component of the wind / east component of the wind)
angle = arctan(46.1 km/h / 240 km/h) ≈ 11.18 degrees
Therefore, the plane's actual direction is approximately 11.18 degrees north of east.