Question
A pilot wants to fly to the North with a ground speed of 120 m/s, so he flies with an airspeed of 120 m/s. Unfortunately, he forgets about the wind: he experiences a 20 m/s wind from the North-West (so at an angle of 45 with respect to the intended heading). For this situation, compute the aircraft's ground speed (in kilometres per hour).
Answers
Using vector addition, we can find the resulting velocity of the aircraft in the North direction and the East direction separately.
The Northward velocity is given by:
v_N = 120 m/s * cos(45) = 84.85 m/s
The Eastward velocity is given by:
v_E = 120 m/s * sin(45) + 20 m/s = 98.88 m/s
Using the Pythagorean theorem, we can find the magnitude of the resulting velocity (ground speed):
v = sqrt(v_N^2 + v_E^2) = 129.49 m/s
Converting to kilometres per hour:
v = 129.49 m/s * 3.6 km/hour/m = 466.16 km/hour
Therefore, the aircraft's ground speed is approximately 466.16 km/hour.
The Northward velocity is given by:
v_N = 120 m/s * cos(45) = 84.85 m/s
The Eastward velocity is given by:
v_E = 120 m/s * sin(45) + 20 m/s = 98.88 m/s
Using the Pythagorean theorem, we can find the magnitude of the resulting velocity (ground speed):
v = sqrt(v_N^2 + v_E^2) = 129.49 m/s
Converting to kilometres per hour:
v = 129.49 m/s * 3.6 km/hour/m = 466.16 km/hour
Therefore, the aircraft's ground speed is approximately 466.16 km/hour.
The ground speed of the aircraft is found by adding the airspeed and the wind. Since these are not in-line, we need to do this in the x- and y-direction separately and then use Pythagoras' theorem to find the total ground speed.
Vx=Vwind * sin(45) = 20 * sin(45) = 14.14m/s
Vx = V - Vwind cos(45) = 120 = 20 * cos(45) = 105.86
Vground = sqrt(Vx^2+Vy^2) = 106.80 m/s
Now that we know our ground speed in m/s we can convert back to km/h:
106.80 m/s * 60 = 6408 m/h
6408 m/h * 60 = 384,480 km/h or 384 km/h
Vx=Vwind * sin(45) = 20 * sin(45) = 14.14m/s
Vx = V - Vwind cos(45) = 120 = 20 * cos(45) = 105.86
Vground = sqrt(Vx^2+Vy^2) = 106.80 m/s
Now that we know our ground speed in m/s we can convert back to km/h:
106.80 m/s * 60 = 6408 m/h
6408 m/h * 60 = 384,480 km/h or 384 km/h
Therefore, the aircraft's ground speed is approximately 384 km/hour.
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