Engineering Mechanics

(^402) „„„„„ A Textbook of Engineering Mechanics
Fig. 19.2.
Example 19.1. A train is moving at 48 km. p.h. and a person sitting in it feels rain coming
down at 60° to the vertical. However, a person standing in a field outside, feels the rain to be
vertical. Find the actual velocity of the rain.
Solution. Given : Velocity of train = 48 km. p.h.
Let us draw the relative velocity and actual velocity
diagrams for the train and rain as shown in Fig. 19.2 and as
discussed below :

1. First of all, draw a line OA representing the actual
   direction of the motion of train which is moving with
   a velocity of 48 km. p.h.


2. Now cut off OB equal to 48 km. p.h. to some suitable
   scale in the opposite direction of the actual motion of
   the train.


3. At O, draw a perpendicular line, which represents the
   actual direction of the rain (or in other words, direction of the rain which is felt by a man
   standing in the field outside).


4. From C, draw a line CB making an angle of 60° with CO (i.e. vertical) which represents
   the relative velocity of the rain.


5. By measurement, we find that the actual velocity of the rain = CO = 27.7 km.p.h.

Mathematical check

In right angled triangle OBC,

48

tan 60

OC

°=

or

48 48

27.7 km. p.h.

tan 60 1.732

OC===

°

Example 19.2. A man, running eastwards with a speed of 6 kilometres per hour, feels the

wind to be blowing directly from North. On doubling his speed, he feels the wind to blow from the

North-east. Find the actual direction and velocity of the wind.

Solution. Given : Velocity of man = 6 km.p.h. (East).

Fig. 19.3.

Let us draw the relative velocity diagram for the man and wind as shown in Fig. 19.3 and as

discussed below :