Engineering Mechanics

(^406) „„„„„ A Textbook of Engineering Mechanics

6. Join the diagonal XR, which gives the magnitude and direction of the relative velocity of
   the two bodies.
   Note. There is no hard and fast rule as to which velocity (in the opposite direction) is to
   be superimposed. Thus any one of the two velocities may be superimposed in the opposite
   direction.
   Example 19.4. A railway coach, having ordinary cross-seats, is travelling at 4 m/s. A
   person runs at 5 m/s on the platform. In what direction, he must run so that he may enter the railway
   coach parallel to the seats? Also find the velocity with which he enters the coach.
   Solution. Given : Velocity of train = 4 m/s and velocity of person = 5 m/s.

Fig. 19.6.

Let us draw the relative velocity diagram of the man and train as shown in Fig. 19.6 and as

discussed below :

1. First of all, draw position of the train having cross-seats. Now draw a line OA representing
   the actual direction of motion of the train with a velocity of 4 m/s.


2. Now cut off OB equal to 4 m to some suitable scale on the opposite direction of the
   actual motion of the train.


3. At O, draw a perpendicular (i.e. parallel to the cross-seats) and cut off BC equal to 5 m
   to the scale, which represents the actual velocity of the man with which he is running on
   the platform.


4. Now OC represents the relative velocity of the man or his velocity with which he enters
   the train. By measurement, we find that ∠ θ = ∠ OBC = 36.8° and OC = 3 m/s Ans.

Mathematical check

In right angled triangle OBC ,

4

cos 0.8

5

θ= = or θ = 36.8°

and OC==(5) – (4)^22 3 m/s Ans.