An airplane is heading due North and its airspeed indicator shows a speed of 300 km/h. If thewind begins blowing from the southwest ([N45oE]) at an average speed of 50 km/h, calculate:a) The velocity of the plane.b) How far off course it will be after 30 min if the pilot takes no corrective action.
Question
An airplane is heading due North and its airspeed indicator shows a speed of 300 km/h. If thewind begins blowing from the southwest ([N45oE]) at an average speed of 50 km/h, calculate:a) The velocity of the plane.b) How far off course it will be after 30 min if the pilot takes no corrective action.
Solution
a) The velocity of the plane:
The velocity of the plane is the vector sum of the velocity of the plane relative to the air and the velocity of the air (wind).
The plane is heading due north, so its velocity relative to the air is 300 km/h in the north direction.
The wind is blowing from the southwest, which is equivalent to blowing towards the northeast. The direction of the wind is therefore 45 degrees east of north.
We can break down the wind velocity into its north and east components. The north component is 50 km/h * cos(45) = 35.36 km/h, and the east component is 50 km/h * sin(45) = 35.36 km/h.
So, the total velocity of the plane is the vector sum of the plane's velocity and the wind's velocity. The north component of the total velocity is 300 km/h (plane's velocity) + 35.36 km/h (wind's north component) = 335.36 km/h. The east component of the total velocity is 0 km/h (plane's velocity) + 35.36 km/h (wind's east component) = 35.36 km/h.
Therefore, the velocity of the plane is 335.36 km/h in the north direction and 35.36 km/h in the east direction.
b) How far off course it will be after 30 min if the pilot takes no corrective action:
The plane will be off course by the distance it travels in the east direction in 30 minutes.
The east component of the plane's velocity is 35.36 km/h. In 30 minutes, which is 0.5 hours, the plane will travel a distance of 35.36 km/h * 0.5 h = 17.68 km.
Therefore, the plane will be 17.68 km off course after 30 minutes if the pilot takes no corrective action.
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