56 



WELLS'S NATURAL PniLOSOPnT. 



Thus, at the end of two seconds, the velocity acquired by a falling body 

 will be twice as great as at the end of one second, thrice as great at the end 

 of the third second, and so on. 



How are bodies ^^^' Bodies projected directly upward, will 

 ^TrSuenTd ^^ influenced by gravitation in their ascent, as 

 by gravity? y^,g|j g^g ^^ their dcscent, but in a reversed 

 order ; producing continually retarded motion while they 

 are rising, and continually increasing motion during their 

 fell. 



Thus, a body projected up perpendicularly into the air, if not influenced by 

 the resistance of tho air, would rise to a height exactly equal to that from 

 which it must have fallen to acquire a final velocity the same as it had at 

 the first instant of its ascent. 



110. To determine the height to which a 

 body projected upward will rise, with a given 

 velocity, ascertain the height from wliich a 

 body would fall to acquire the same velocity. 

 The answer in one case will be the answer in 



How can we 



determine the 

 height which a 

 body projected 

 upward with a 

 given velocity 

 will ascead ? 



the other. 



How do the 

 times of ascent 

 and descent 

 compare i 



111, The time, also, which the ascending 

 body would require to attain its greatest 

 height, would be just equal to the time it 

 would require to fall to the ground from that height. 



The following table exhibits an analysis of the motions of a falling body; 

 the spaces passed over in each interval of time of falling, increasing as tho 

 odd numbers 1, 3, 5, 7, 9, etc. ; the velocities acquired at the end of each in- 

 terval increasing directly as tho times ; and uhe whole space passed over being 

 as tho squares of tho times. 



Where extreme accuracy is not required, most of the problems connected 

 with the descent of falling bodies, may be worked with great readiness — 16 



