Engineering Mechanics

(^414) „„„„„ A Textbook of Engineering Mechanics
Consider two bodies A and B moving with velocities vA and vB respectively. Let the actual
directions of vA and vB be as shown in Fig. 19.15 (a).
Fig. 19.15.
Now in order to find the time for exchange of signals, first of all we have to find the relative
velocity of one body with respect to the other. Let us draw the relative velocity diagram XMRN for
the two bodies as usual, in which XR represents the relative velocity as shown in Fig. 19.15 (b).
Fig. 19.16. Exchange of signal diagram
Now let us draw the exchange of signal diagram for the two bodies with the help of their
relative velocity diagram as shown in Fig. 19.16 and as discussed below :

1. First of all, extend the relative velocity line XR to L.


2. Now cut off XQ equal to the distance between two bodies, at any given instant, to the
   scale.


3. With Q as centre and radius equal to the vision distance, draw an arc meeting the relative
   velocity line at P 1 and P 2.


4. The time for exchange of signals is to the time required by the body B to travel from P 1 to
   P 2 is given by the relation :
   Distance 2 to the scale
   Relative velocity of two bodies

XP

=

• Distance^1 to the scale
  Relative velocity of two bodies

XP

Notes : 1. A little consideration will show that the two bodies will go on coming nearer to

each other till the body B reaches P 1 (i.e. within the vision distance). At this point, the bodies will start

exchanging signals.They will continue till the body B reaches the point P 2. Beyond this point, the two

bodies will be beyond the vision distance.

2. Such problems should, preferably, be attempted graphically.
   Example 19.9. Two ships A and B are moving with velocities of 12 km.p.h. in North and
   20 km.p.h. in North-East directions respectively. At midnight, the ship A is 40 km East of B. If they
   can exchange signals when they are 10 km apart, find when they will begin to signal and how long
   they will continue?