Chapter 19 : Relative Velocity 405
EXERCISE 19.1
- A passenger, travelling in a train, observed the drops of rain water to pass the railway
carriage at an angle of 10° 18' with the horizontal. If actual velocity of the water drops is
2 m/s, show that the train is moving at 39.6 km.p.h. Assume actual direction of the train to
be vertical. - A shower of rain appears to be falling vertically downwards with a velocity of 12 km.p.h.
to a man walking due to West with a velocity of 5 km.p.h. What is the actual velocity and
direction of the rain? (Ans. 13 km.p.h.; 23°)
19.4.RELATIVE VELOCITY OF TWO BODIES MOVING ALONG INCLINED
DIRECTIONS
Sometimes, two bodies are moving along two inclined directions. In such a case, the relative
velocity of one, with respect to the other, may be found out by superimposing the actual velocity of
any one of these two bodies, in the opposite direction, on both the bodies. It will be interesting to
know that after superimposing the velocity, one of the bodies will be brought to rest. And the resultant
of the two velocities, on the second, will give the required relative velocity.
(a) Actual velocity diagram (b) Relative velocity diagram.
Fig. 19.5. Bodies moving along inclined directions.Now consider two bodies A and B moving with velocities vA and vB respectively along East
and North as shown in Fig. 19.5 (a).
Now let us draw the relative velocity diagram as shown in Fig. 19.5 (b) and as discussed
below :
- First of all, draw East, West, North and South lines meeting at X.
- Since the body A is moving eastwards, therefore cut off XL equal to velocity vA to some
suitable scale towards East, representing the actual velocity of the body A. - Now cut off XM equal to the velocity vA to the same scale on the opposite direction of
the actual motion of the body (i.e. towards West ). - Now cut off XN equal to the velocity vB to the scale to represent the actual velocity of
the body B. - Complete the parallelogram XMRN with XM and XN as adjacent sides.