66 MOTION OF PROJECTILES. 



the third, and 39*4, which is the velocity at the end of 



29*6 -f 39*4 

 the third second ; hence it is r = 34 m *5. 



jU 



The spaces passed over in each second are obviously 

 equal to the average velocities in each second, and the 

 total space traversed in two or more seconds is found 

 by adding together the spaces traversed in the separate 

 seconds. Thus we find the space traversed in two 

 seconds to be 14'9 + 24 -7 = 39 m '6, in three seconds 

 39*6 -f 34*5 = 74 m .l, numbers which agree with those 

 above found by a different reasoning. 



If a body be thrown vertically upwards, the force of 

 gravity will diminish its velocity by the same amount 

 as that by which it was increased when it was projected 

 downwards. If we suppose a body to be thrown upwards 

 with a velocity of 29 m< 4, it will after one second have a 

 velocity of only 29*4 9'8 = 19 m *6, after two seconds 

 of 19-6 - 9-8 = 9 m -8, and at- the end of the third 

 second its velocity is completely destroyed; the body 

 will at this instant cease to move upwards and will 

 begin to fall; it has reached the greatest height to 

 which it can ascend. The velocity of a body projected 

 vertically upwards is thus diminished by 9 m *8 in every 

 second, and the time which elapses after the beginning 

 of the upward motion until it ceases is hence easily 

 found by calculating how many times 9*8 is contained 

 in the initial velocity ; or, in other words, the time re- 

 quired by a body projected vertically upwards for reaching 

 the highest point is found by dividing the velocity of projec- 

 tion by the acceleration of gravity. The time of ascent 



for a velocity of projection of 98 m is thus found to be 

 ijg 

 = 10 seconds; for a velocity of 12 m *25 it is 



J.o 



