Final answer:
The magnitude and direction of velocity relative to the Earth are determined by vector addition of an object's velocity and the motion of the medium it moves through, such as wind or currents.
Step-by-step explanation:
The magnitude and direction of an object's velocity relative to the Earth depend on both the object's speed and direction of travel, as well as any additional motion of the medium through which it is moving, such as air or water currents.
For the airplane example, to find the airplane's speed relative to the air, we need to consider both the plane's airspeed and the speed and direction of the jet stream. The airplane's velocity relative to the Earth can be found by vector addition of the airplane's velocity relative to the air and the jet stream's velocity. For the case of the sailboat in a current and encountering wind, the sailboat's velocity relative to the water is the vector sum of the sailboat's velocity relative to the Earth and the wind's velocity relative to the Earth, taking into account the respective directions of the current and wind.
The velocity of an object relative to the Earth can be described by a magnitude, measured in meters per second (m/s), and a direction, which can be reported in degrees relative to a compass direction (e.g., degrees south of east).