Chapter 19 : Relative Velocity 401
to an observer on the earth, is 50 kilometres per hour. Thus the relative velocity of A with respect to
B, is the velocity with which A appears to move to an observer sitting on B, neglecting the motion of
B relative to the Earth.
19.2.METHODS FOR RELATIVE VELOCITY
The relative velocity of two bodies may be found out either graphically or analytically. But it
has been experienced that analytical method is somewhat confusing. Thus in this book, we shall
follow the graphical method. The best practice is the combination of both the methods. The values
should first be obtained by graphical method and then their accuracy should be checked analytically.
19.3.RELATIVE VELOCITY OF RAIN AND MAN
We see in our daily walk of life, that whenever we go out in rain, we have to adjust the inclination
of our umbrella (with the vertical) to protect ourselves from the rain. If the rain is falling in the
opposite direction of our movement, then the inclination of umbrella is less when we are standing,
than that when we are moving. This happens because the relative velocity of rain (with respect to our
movement) now is inclined at a greater angle.
(a) Actual velocity diagram (b) Relative velocity diagram
Fig. 19.1.
Now consider CO and OA as actual directions of the rain and man respectively as shown in
Fig. 19.1 (a). The relative velocity diagram for rain and man may be drawn as shown in Fig. 19.1 (b)
and as discussed below :
- First of all, draw a horizontal line OA to some suitable scale which represents the actual
direction of motion of the man. - Now draw CO equal to the velocity of the rain (assumed to be vertical in this case) to the
scale. - Let us *superimpose a velocity equal and opposite to that of the man on both the man as
well as rain. It will reduce the velocity of the man to zero. And the rain will have some
resultant velocity (due to its own velocity and superimposed velocity) as shown in Fig.
19.1 (b). - Now relative velocity of the rain and man, in magnitude and direction, will be given by the
resultant velocity CB, which may be found out either graphically or by Triangle Law or
Forces.
* If the velocity of man is superimposed on both the man and rain, their relative velocity remains unchanged.