3.4 Resultant motion

Motion of an object in a medium like air, water or other moving body is affected by the motion of the medium itself. It is all so evident on a flight that the aircraft covers the same distance faster or slower, depending on the wind force working on it. The motion of aircraft is influenced by the velocity (read force exerted by the wind) of the wind - in both its magnitude and direction.

Similarly, the motion of boat, steamer or sea liner is influenced by the velocity of water stream. We can analyze these problems, using concept of relative motion (velocity), but with certain specific consideration.

Understanding motion in a medium

First thing, we note that two bodies under consideration in the study of relative motion are essentially separated bodies. This is not so here. The body moves right within the body of the medium. They are in contact with each other. The body, in question, acquires a net velocity which comprises of its own velocity and that of the medium. Importantly, the two mass systems are in contact during motion unlike consideration in relative motion, where bodies are moving separately.

Resultant motion

The velocity of a boat in a stream, for example, is the resultant of velocities of the velocity of boat in still water and the velocity of the stream. The boat, therefore, moves having resultant velocity with respect to ground reference. This is the velocity with which boat ultimately moves in the stream and covers distance along a path.

The important point here to understand is that all velocities are measured in ground reference. The velocity of boat in still water is an indirect reference to ground. Velocity of stream, ofcourse, is measured with respect to ground. The resultant velocity of the boat is what an observer observes on the ground.

$$\begin{array}{l}{\mathbf{v}}_R={\mathbf{v}}_B+{\mathbf{v}}_W\end{array}$$

where “ ${\mathbf{v}}_R$ ” is the resultant velocity of the object; “ ${\mathbf{v}}_B$ ” is the velocity of the boat in still water. and “ ${\mathbf{v}}_W$ ” is the velocity of the water stream.

The question now is that if velocities of entities are all measured with respect to a common reference, then where is the question of relative motion? We can simply treat the velocity of the body as seen from the ground equal to the resultant velocity, comprising of velocity of the object in a standstill medium and velocity of the medium itself.

Resultant velocity and relative velocity

This interpretation or understanding of resultant motion is perfectly valid except when a problem situation specifically involves terms such as “relative speed of boat with respect to stream” or “relative velocity of an aircraft with respect to air”. The big question is to identify whether this relative velocity refers to the resultant velocity or the velocity of the object in still medium. We can understand the importance of reference to relative velocity by interpreting some of the problems as given here (we shall work these problems subsequently) :