68 MOTION OF PROJECTILES. 



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It appears from column 5 that the height of as< 

 is found by multiplying the velocity of projection by itself, 

 and dividing the resulting square number by twice the ac- 

 celeration of gravity (2 x 9' = 19'6). The truth of 

 this rule is easily seen. By dividing the velocity of 

 projection by the acceleration the time of ascent is 

 found, and this time must again be multiplied by the 

 velocity of projection, in order to find the height 

 which the body would reach if it were uninfluenced by 

 gravity ; hence instead of first dividing the velocity of 

 projection by the acceleration, and multiplying the 

 quotient again by the velocity of projection, the velo- 

 city of projection may be at once multiplied by itself 

 and divided by the acceleration. But the height thus 

 found is, as appears from a comparison of columns 3, 4, 

 and 5, always twice as great as that actually reached, 

 hence it follows that the actual height is equal to the 

 square of the velocity divided by twice the acceleration. 

 If this table be compared with the two small tables 

 given at the end of the last paragraph, further simple 

 relations will appear. For instance, a body falls in six 

 seconds through a space of 176 m *4 and acquires a 

 velocity of 58 m< 8 ; conversely, a body projected with a 

 velocity of 58 m *8 ascends for six seconds and reaches a 

 height of 176 m *4 ; and the same relation holds for any 

 other velocity of projection. The velocity which a body 

 acquires in falling through a certain height is always equal 

 to the velocity with which the body must be projected 

 upwards in order to reach the same height. A body 

 projected upwards and having reached the greatest 

 height is then for an instant at rest, after which it 

 begins again to fall freely ; it follows that a body ac~ 



