338 PRACTICAL MATHEMATICS 



At the highest point the velocity is evidently 0, 

 and tan y.gt = <xu 



agt = tan" 1 ocu 



t = tan- 1 <x.v 



ds I A 



Also v = -77 = - tan (0 agt) 



at a 



and s = -\ tan (0 v.gt) dt + Const 



J 



= s- log e sec (0 a^i) + Const 



but when t = 0, s = 0, and = r- log e sec 6 + Const 



a 



Hence s = ^{log e sec - log e sec (0 - agt) } 



I sec 



?g 38 sec (0 - <x.gt) 



JLinP- cos ( 9 ~ a ^) 

 v?g Ke cos 



The vertical distance of the highest point above the point c 

 projection will be obtained when t = tan -1 oo> ; that is, whei 



Then h = log e sec 



but tan = ajy and sec = Vl + 



Hence h = log e (1 + oc 2 



171. The Compound Interest Law. 



\fitl 



Then I = n \dx + Const 



Jy J 



and log e y = nx + c 



y = 6 +c 



where A = e 



