imottY OF THE MOTiaNF tti^ llC^CK^W* 24f 



Iff 

 2 (/ — up) 



Sec. j r = (when t =z a) j. \ a ^ 



( 



^ w 



2 w 

 1 (/ — ap) X (^ — fly) 



tu+1 ]<iW'\-U.l^ '^ {3w + ij.l*"^ ' 



(3t» + 1) . /*'*' y ? V'^ + 1 2w+l 



4- — , $z'\^i ? for the s^pace de«cribed by thef^ 



^ 3u; + 1 y 5 



rocket at the end of the time /. 



Now to determine how far the rocket wiU farther move 

 before its motion is wholly destroyed. Put a =: the velocity^ 

 at the end of its burning = 2820*325 feet per second, and 

 V any variable velocity corresponding to the space x; w zz 

 weight of the rocket =: 448ozs., and R = '0002343 ounces^ 

 the resistance of the medium to the rocket when moving 

 with a velocity of 1 foot, per second. Then R i>* will be the 



R »* 



resistance to velocity v, and the force by which the 



rocket is retarded by the fluid. Hence 4- = r-rr = -^ 



. and X r: "^^ — rr • hyp. log. v ; and the fluent 

 2gR 



. hyp. log. a. Which by substitution 



2gR 



efnumbersis = 305170'3 feet. 



Hence it appears, that, after the burning of the rocket Space de- 

 ceases, it will move to a distariceof 305 170''3 feet, or nearly 58 *c"bed. 

 miles, before all its motion is destroyed, when it will remain 

 at rest in the medium ; there being no force to influence it 

 in any manner or direction whatever, and having no power 

 to create motion in itself. 



As to the lime that the rocket would be in movingthrough Timeof mov- 

 this space, it -will be had as follows. The same substitution ing through it. 

 as above being retained; the general fluxional expression 



for the time [t') namely will be found n 



2^/ 2gRo* 



