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Question

A small airplane flies at a velocity of 145 km/h toward the south as observed by a person on the ground. The airplane pilot measures an air velocity of 172 km/h south. What is the velocity of the wind that affects the plane?

Answer 1

Assuming there's no other information available this is a fairly simple question. The pilot is showing a speed of 172 kph, while his actual speed over the ground is only 145 kph, this indicates that wind is slowing him down, because the airspeed sensor measures the speed of the relative wind around the plane. So if the plane is moving forward at 145 kph the wind must be moving towards the plane at a speed of 27 kph to register an airspeed of 172 kph. The opposite affect is observed when a tailwind is present. This is why planes like to takeoff and land with a headwind and not a tailwind, they can have a higher airspeed with a headwind (thus allowing the to not stall), but have a lower groundspeed (thus allowing an easier landing). A tailwind is preferred when enroute because it allows the plane to fly faster than with just the thrust provided by the engines alone.