An airplane tracks due north over the ground in a wind at altitude of 20 m/s due

Question

An airplane tracks due north over the ground in a wind at altitude of 20 m/s due east. The plane's airspeed is 95 m/s directed slightly west of north. What is the resulting ground-speed in m/s? An airplane tracks due north over the ground in a wind at altitude of 20 m/s due east. The plane's airspeed is 95 m/s directed slightly west of north. What is the resulting ground-speed in m/s? An airplane tracks due north over the ground in a wind at altitude of 20 m/s due east. The plane's airspeed is 95 m/s directed slightly west of north. What is the resulting ground-speed in m/s?

Explanation / Answer

Here,

speed of plane relative to air , vp = 95 m/s

speed of air , va = 20 m/s

Now, as the plane is going towards north relative to ground

resultant ground speed = sqrt(vp^2 - va^2)

resultant ground speed = sqrt(95^2 - 20^2)

resultant ground speed = 92.9 m/s

the resultant ground speed of the plane is 92.9 m/s

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