Engineering Mechanics

Chapter 19 : Relative Velocity „„„„„ 407

Example 19.5. Two ships leave a port at the same time. The first steams North-West
at 32 kilometres per hour and the second 40° South of West at 24 kilometres per hour.

(a) What is the velocity of the second ship relative to the first in km per hour?
(b) After what time, they will be 160 km apart?
Solution. Given : Velocity of first ship 32 km.p.h. (N-W) ; Velocity of second ship = 24
km.p.h. (40°^ South of West).

(a) Velocity of the second ship relative to the first

Fig. 19.7.
First of all, let us draw the actual velocity diagram of the two ships as shown in Fig. 19.7 (a).
Now draw the relative velocity diagram as shown in Fig. 19.7 (b) and as discussed below :

1. First of all, draw the East, West, North and South lines meeting at O.


2. Since the first ship steams in the North-West direction , therefore, draw a line OA at 45°^ to
   the North (or West) representing the actual direction of the ship at 32 km.p.h.


3. Now cut off OB equal to 32 km to some suitable scale on the opposite direction of the
   actual motion of the first ship (i.e. South-East).


4. Now draw a line at an angle of 40°^ South of West and cut off OC equal to 24 km to the
   scale to represent the actual direction of the second ship.


5. Complete the parallelogram OBRC with OB and OC as adjacent sides.


6. Join OR ,which gives the magnitude and direction of the second ship relative to the first.
   By measurement, we find that OR = 38.3 km.p.h. Ans.

(b) Time when the two ships will be 160 km apart

We know that the two ships will be 160 km apart after

160

4.18 hrs

38.3

== Ans.

Mathematical check

In parallelogram OBRC

OR= (32)^22 ++××(24) 2 32 24 cos 95°