LAWS OF FALLING BODIES. 55 



Aov doea 104 -'WhGn a body falls, it is attracted by gravity during 



f^ijH^body" ^^^ '^^^^^ *""® °^ i*3 falling. Gravity does not merely set 

 the body in motion and then cease, but it continues to act. 

 During the first second 'of time, the force of gravity will cause the body to 

 descend through a certain space. At the end of this time, the body would 

 continue to move, with the motion it has acquired, without the action of any 

 further force, merely on account of its inertia. But gravity continues to act, 

 and will add as much more motion to the falling body during the second 

 second of time, as it did during the first second, and as much again during 

 the third second, and so on. I 



_, , . ,^ 105. Fallinoj bodies, therefore, descend to 



what IS the . . 



jaw of fauing tliG cartli witli ft uniform accelerated motion. 



bodies ? • n 



A body falling from a height will fall 16 feet 

 in the first second of time/^ three times that distance in 

 the second, five times in the third, seven in the fourth, 

 the spaces passed over in each second increasing as the 

 odd numbers 1, 3, 5, 7, 9, 11, etc. 



How does the 106. The entire space passed over by a body 

 over aifd ^tht i° ftiUing is as the square of the time ; that is, 

 Ji»\^^^^!fi'' in twice the time it w^ill fall through four times 



ing body com- o 



p*'^^ the space ; in thrice the time, nine times the 



space. f 



The time occupied in falling, therefore, being known, the height from which 

 a body falls may be calculated by the following rule : 



107. Multiply the square of the number of 



Time being / •' •»■ . ^ , . 



giTun, how- can sccouds of time consumed in falhng, by the 



tlieheightfrom •n /> ii • i x> 



which a body distancB wIl zh. a body will fall in one second oi 



falls be found 1 . •' 



time. 



Thus, a stone is five seconds in falling from the tep of a precipice ; the square 

 of five seconds is 25; this multipUed by 16, the number of feet a body will 

 MI in one second, gives 400 — the height of the precipice. 



How do the 108. As the effect of gravity is to produce a 

 Hm^esoffaiung uuiform accelcratcd motion, the velocity of % 

 iomparer falling body will increase as the time increases. 



• The spaces described by falling bodies are here given in round numbers, the fractions 

 being omitted. The space described by a falling body during the first second is 16 1-lOth 

 feet. 



t The resistance of the air essentially modifies the laws of the motions of falling bodies, 

 as here stated, and with a certain velocity, will become equal to the weight of the falling 

 body. After this takes place, the body will descend with a uniform velocity. There 

 Is, therefore, a limit to the velocity which a body can acquire by falling through the 

 «tmosphrve. 



