Chapter 19 : Relative Velocity 413
- Now cut off XN equal to 15 km to the scale on the North line to represent the actual
direction of the second ship. - Complete the parallelogram XMRN with XM and XN as adjacent sides.
- Join XR which gives the magnitude and direction of the second ship relative to the first.
By measurement, we find that XR = 21.2 km.p.h. and ∠ θ = 45°.
Fig. 19.14. Closest velocity diagram
Now let us draw the closest velocity diagram as shown in Fig. 19.14 and as discussed below :- First of all, draw the relative velocity diagram and the parallelogram XMRN as discussed
above. Now extend the relative velocity line XR to L. - At noon, let the second ship be at X. Therefore the first ship will be 15 × 1.5 = 22.5 km
towards North or in other words, the second ship will be 22.5 km behind the first (i.e.
towards South). So mark XP equal to 22.5 km to the scale. - From P, draw PQ perpendicular to XL. which gives the closest distance between the two
ships. By measurement we find that PQ = 15.9 km. Ans.
Time when the ships will be closest together
By measurement we also find that XQ = 15.9 km. Therefore time taken by the second ship to
reach Q from X
15.9
0.75 hr 45 min
21.2== =Thus the two ships will be closest together at 12.45 P.M. Ans.19.6.TIME FOR EXCHANGE OF SIGNALS OF THE TWO BODIES MOVING
ALONG INCLINED DIRECTIONS
We have discussed in Art. 19.5 that whenever two bodies are moving in different directions, at
a certain instant they are least distance apart. It will be interesting to know that before and after this
instant, the two bodies are not at the least distance apart. It is thus obvious, that the bodies start
coming nearer to each other, and after coming at the least distance apart, they start going away from
each other.
Sometimes, these bodies start exchanging signals, whenever they come within the vision of
each other, and go on signalling so long as they remain within their vision. The moment they are
beyond their vision, the bodies stop exchanging of signals. Thus the time for exchange of signals of
the two moving bodies, is the time for which they remain within their vision.