MOTION OF PROJECTILES. 65 



1 1 . Motion of Projectiles. When a body, capable of 

 moving freely in ever} T direction, is acted on by several 

 forces at the same time, each force will produce pre- 

 cisely the same effect as if it acted alone. If a body is 

 thrown from the hand, it maintains the velocity hereby 

 acquired, by its inertia, but is at the same time acted 

 on by gravity. A stone thrown vertically downwards 

 from a tower with a velocity of 10 m per second, would 

 pass in one second through 10 m , in two seconds through 

 20 m , etc., if there were no force of gravity. But, as has 

 been shown in the preceding article, gravity causes the 

 body to move downwards in one second through 4 m *9, 

 in two seconds through 19 m< 6, etc. The body will 

 hence move in the first second through 10 -f 4 m< 9 = 

 14 m -9, in two seconds through 20 -f 19*6 = 39 m '6, in 

 three seconds through 30 -f 44' 1 = 74 m 'l, 30 m being 

 le to the force with which the body has been pro- 

 bed, and 44 m *l to the force of gravity. 

 The velocity of a falling body increases in every 

 second by 9 m> 8. If the velocity of the stone when it 

 leaves the hand be 10 m , it will be at the end of the first 

 second 10 + 9'8 = 19 m '8; at the end of the second 

 I second it will be 10 + 2 x 9'8 = 29 m '6, and at the end 

 of the third second 10 + 3 x 9-8 = 39 m '4. The 

 I average velocity with which the body moves in the 

 first second is the arithmetical mean of 10 and 19*8, 



viz., = 14 m '9 ; the average velocity of the 



second second is the mean of 19'8 and 29'6, viz., 



a - - = 24 m< 7; the average velocity during the 



4 



third second is similarly the mean of 29*6, which is the 

 velocity at the end of the second second, or beginning of 



F 



