So that Denoting dx/dt, the horizontal component of the velocity, by q, (49) v cos i =q, equation (43) becomes (50) dq/dt= -r cos i, and therefore by !(48) (51) dq _dq dt ry di - dt di-g' It is convenient to express r as a function of v in the previous notation (52) Cr = f(v), dq _vf(v) di - Cg ' an equation connecting q and i.
The particle comes to rest when V us Vf I Uo2\
Comparative Motion of Two Pistons.If there be but two pistons, whose areas are af and af, and their velocities Vf and vI, their comparative motion is expressed by the equation V2/Vf = aia/2; (2)
In order to produce a retardation from the greater velocity~ v2 to the less velocity Vf, it is necessary to apply to the body a resistance connected with the retardation and the time by an equation identical in every respect with equation (71), except by the substitution of a resistance for an effort; and in overcoming that resistance the body performs work to an amount determined by equation (72), putting Rds for Pas..