DYNAMICS. 47 



91. The greatest height to which a heavy body 

 can ascend, when projected directly upwards with 



c 2 

 the velocity c, is ^ , the same height from which 



it must have fallen to acquire the velocity c ; and 

 in all points, both of its ascent and descent, the re- 

 lation between the time and the height h is ex- 

 pressed by the equation h=ct ^g t*. 



For the space through which the body would have as- 

 cended, with the velocity c in the time t, is ct; 

 from which the retardation produced by the action 

 of gravity in the same time, that is \ g / 2 , ( 87. b) 

 must be taken away. 



c 



_ . 

 . This equation gives t - -f - ^/c 2 %gh. The 



cJ O 



reason why two different values of t correspond to 

 the same value of h is, that the body is at the same 

 height at two different times, one in its ascent, and 

 another in its descent. 



1). The sum of the two values of t is , or twice the 



g 



time of the total ascent. 



The difference between them is - L/C* 





92. If two bodies A and B, of which A is 

 the heavier, be suspended over a pulley move- 



able 



