When flying an airplane, you can completly forget everything about groundspeed. A airplane flies using air, so you have to use airspeed instead.
Ex: A Cessna 182 is parked on a ramp and the groundspeed is obviously 0 kts. But then there is a wind coming head-on to the aircraft at 15 knots. Now the IAS is 15 knots even though the groundspeed is zero knots. This is why you always tie down smaller props. If for some reason a 60 knot headwind comes at a C152 while it is parked on a ramp without being tied down, it would lift off the ground because the airspeed is 60 kts while the groundspeed still is 0 kts and at 60 kts, a C152 would fly.
If you have a tailwind, the Groundspeed will increase even though the IAS stays the same because the engines are still producing the same amount of thrust. If you want to increase the IAS, you have to use more thrust.
How does the pitot tube figure this out ?
The pitot tube doesn´t calulate the groundspeed, it only calculates the IAS.
Fritzi