172 Dynamics. 



Thus, if I would know, for example, from what height a heavy 

 body must fall, to acquire a velocity of 100 feet in a second, I 

 divide the square of 100, namely, 10000, by 64,4 ; and the quo- 

 tient VT,T = 155,2&c., is the height through which a body 

 must fall to acquire a velocity of 100 feet in a second. 



We might evidently make use of the same formula in deter- 

 mining to what height a body would rise, when projected verti- 

 cally upward with a known velocity. 



Moreover, from the above equation, s = we obtain 



v 2 = 2g 5, or v = \/2 g s 1= 8,024 v*r 



that is, the velocity acquired in falling through any space s, is 

 equal to \-'2~F* or equal to eight times the square root of s nearly, 

 u, g, and s, being estimated in feet. Thus the velocity acquired 

 in falling through 1 mile or 5280 feet, is equal to 



8,024 v*<*o = 583 feet very nearly. 



278. By these examples it Avill be seen that all the circum- 

 stances of the motion of heavy bodies may be easily determined ; 

 and it is accordingly to these motions, that we commonly refer 

 all others ; so that instead of giving immediately the velocity of 

 a body, we often give the height from which it must fall to ac- 

 quire this velocity. Occasions will be furnished for examples 

 hereafter. 



We will merely observe, therefore, by way of recapitulation, 

 that all the circumstances of accelerated motion, and consequent- 

 ly of the motion of heavy bodies, are comprehended in the two 

 equations v = g J, s = ^ g t 2 ; so that, g being known, and one 

 of the three things, f, s, i>, or the time, space, and velocity, the 

 two others may always be found, either immediately by one or 

 the other of the above equations, or by means of both combined 

 after the manner of article 277. 



279. When a body is subjected to the action of a force that 

 is exerted upon it without interruption, but in a different manner 

 at each successive instant, we give to the motion the general de- 

 nomination of varied. We have examples of varied motion in 

 the unbending of springs ; although in this case the velocity goes 



