Engineering Mechanics

Chapter 19 : Relative Velocity „„„„„ 411

From the geometry of the figure, we find that in triangle XPQ, XQ = 18.1 m, QP = 200 m
and ∠ PXQ = 30° + 36.9° = 66.9°. Now using the sine rule,

sin sin

XQ QP

XPQ PXQ

=

∠∠

18.1 200 200

217.4

sin XPQ sin 66.9 0.9198

===

∠

or

18.1

sin 0 0833 or 4 8

217.4

∠= =⋅XPQ ∠=⋅°XPQ

∴ Angle, at which rifleman should aim,

α = 30° + 4.8° = 34.8° Ans.

EXERCISE 19.2

1. A train moving at 30 km.p.h. is struck by a stone moving at right angles to the train with a
   velocity of 22.5 km.p.h. Find the velocity and direction which the stone appears to strike
   the train, to a person sitting in it. (Ans. 37.5 km.p.h. ; 53°)


2. If a ship is moving North-West at 15 knots and a second ship is moving due East at 7
   knots, determine the direction and magnitude of the second ship relative to the first.
   (Ans. 31° ; 20.6 knots)


3. A man is sitting in a ship (S 1 ) sailing South-East with a velocity of 12 km.p.h. He notices
   another ship (S 2 ) which always appears to him to be in the East and going further away. If
   the speed of the ship (S 2 ) is 18 km.p.h., find the direction of ship (S 2 ). (Ans. 28°)


4. A steam ship is travelling North at the rate of 20 km.p.h. and there is a wind blowing from
   North-East at 30 km.p.h. Find the direction in which the smoke from the chimney will
   appear to an observer sitting in the ship. (Ans. 27°)

19.5. LEAST DISTANCE BETWEEN THE TWO BODIES MOVING ALONG
INCLINED DIRECTIONS

Fig. 19.12.
Consider two bodies A and B moving with velocities vA and vB respectively. Let the actual
direction of vA and vB be as shown in Fig. 19.12 (a).