Final answer:
The resultant velocity vector of an airplane flying east at 100 km/h with a 50 km/h tailwind is 150 km/h east. This is found by simply adding the tailwind's velocity to the airplane's airspeed, as both are in the same direction.
Step-by-step explanation:
To calculate the resultant velocity vector of an airplane flying east at 100 km/h with a 50 km/h tailwind, we must add the velocity of the airplane to the velocity of the wind. Since the wind is a tailwind, it is in the same direction as the airplane's motion, therefore we can directly add the magnitudes of the two velocity vectors. The resultant velocity vector is the sum of the airplane's airspeed and the wind speed.
The airplane's airspeed = 100 km/h
The tailwind's speed = 50 km/h
Resultant velocity = Airplane speed + Tailwind speed = 100 km/h + 50 km/h = 150 km/h east.
A vector representation would show a horizontal arrow pointing to the right (East) for the airplane's velocity, a smaller arrow in the same direction for the tailwind, and a longer arrow representing the sum of the two for the resultant velocity.