pedo with reference to the ship from which it is projected may be written 3vt, and the velocity of the ship with reference to the enemy maybe written ,,
,,. In Fig. 7, OA represents viand OB represents nvs. We notice that in these symbols for the velocities which we have compounded, the right subscript of one velocity is the same as the left subscript of the other, and that the resultant has the two subscripts that are different. In our example, svi and nvs combined give the velocity of the torpedo with respect to the enemy, nvt.
If we have given ,vt and nvs and wish svt we need only notice that nvs = -sv,,. Thus, we can compound ,,v, and -,vn thereby obtaining svt.
The " torpedo director " consists of two rods variable in length and direction which are linked together and to a third rod carrying a telescope. The telescope points in the direction vi when the other two rods are adjusted to represent in direction and length sit and nvs. When the enemy ship arrives at C, Fig. 7, it is seen in the telescope fastened to the rod OC. At this instant the torpedo is launched in the direction and with the speed relative to the firing ship represented by OA. The torpedo meets the enemy ship at A.
If, however, we attempt to combine in this manner two velocities which do not have a right subscript of one the same as a left subscript of the other, we shall have a result which is without meaning. For example, if we attempt to combine the velocity of the torpedo with respect to the enemy and the velocity of the firing ship with respect to the enemy, we would get the line OD', Fig. 8. This line has no physical meaning.
Problem. Waves are moving across the sea with a velocity of one knot westward, relative to the earth. The distance between the crests is 50 ft.