In like manner a body thrown perpen dicularly upward, as a ball from a can non, will have its motion continually re tarded, because gravity acts constantly upon it in a direction contrary to that giv en it by the powder; so that its velocity upwards must be continually diminished, and its motion as continually retarded, till at last it be all destroyed. The body has then attained its utmost height, and is for a moment motionless, after which it begins to descend with a velocity in the same manner accelerated, till it comes to the earth's surface.
Since the momentum (M) of a body is compounded of the quantity of matter (Q), and the velocity (V), we have this general expression M = Q V, for the force of any body, A ; and suppose the force of another body, B, be represent ed by the same letters in italics, viz. M= Q V.
Let the two bodies, A and B, in mo tion, impinge on each other directly ; if they tend both the same way, the sum of their motions towards the same part will be Q V -I- Q V But if they tend towards contrary parts, or meet, then the sum of their motions towards the same part will be Q V — Q for since the motion of one of the bodies is contrary to what it was before, it must be connected by a contrary sign. Or thus; because, when
the motion of B conspires with that of A, it is added to it; so, when it is contrary, it is subducted from it, and the sum or difference of the absolute motions is the whole relative motion, or that which is made towards the same part. Again, this total motion towards the same part is the same, both before and after the stroke, in case the two bodies, A and B, impinge on each other ; because, what. ever change or motion is made in one of those bodies by the stroke, the same is produced in the other body towards the same part: that is, as much as the motion of B is increased or decreased towards the same part by the action of A, just so much is the motion of A diminished or augmented towards the same part by the equal re-action of B, by the third law of motion.
In bodies not elastic, let s be the velo city of the bodies after the stroke, (for, • since we suppose them not elastic, there can be nothing to separate them after collision ; they must therefore both go on together, or with the same celerity.) Then the sum of the motions after colli sion will be Qs+ Qx; whence, if the bodies tend the same way, we have Q V or if they meet, Q V— Q V=Qx+Qx; and accord ingly, Q V ± Q V x, er