a small plane is traveling due south a t a velocity of 90 m/s. It suddenly encounters a tailwind of 27 m/s heading due south. what is The "air velocity" of the plan stays the same....but what is the resultant velocity (aka..."ground velocity") of the aircraft?
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The air velocity is indeed still +90 m/s (due south).
The velocity with reference to ground is
Vg=+90+(-27)=63 m/s (due south).
Think of the plane moving south for 90 m in one second, and head wind blows it back towards north by 27 m, also in one second, so the net/ground velocity is therefore 90-27=63 m/s.
To determine the resultant velocity or ground velocity of the aircraft, we need to consider the effect of the tailwind on the plane's motion.
The plane is initially traveling due south with a velocity of 90 m/s. The tailwind is also heading due south with a velocity of 27 m/s. Since the tailwind is blowing in the same direction as the plane's motion, it will add to the plane's velocity.
To find the resultant velocity, we can add the velocities of the plane and the tailwind since they are in the same direction. Mathematically, we can calculate it as:
Resultant velocity = Plane's velocity + Tailwind's velocity
Ground velocity = 90 m/s + 27 m/s
Ground velocity = 117 m/s
Therefore, the resultant velocity or ground velocity of the aircraft is 117 m/s, given the plane's velocity of 90 m/s and a tailwind of 27 m/s, both heading due south.