RULES RELATING TO THE VELOCITY OF FALLING BODIES.
1.—To find the Velocity a falling Body will acquire in any given time.
Multiply the time, in seconds, by 321⁄6, and it will give the velocity acquired in feet, per second.
Example. Required the velocity in seven seconds.
321⁄6 × 7 = 2251⁄6 feet. Ans.
2.—To find the Velocity a Body will acquire by falling from any given height.
Multiply the space, in feet, by 641⁄3, the square root of the product will be the velocity acquired, in feet, per second.
Example. Required the velocity which a ball has acquired in descending through 201 feet.
641⁄3 × 201 = 12931; √12931 = 113·7 feet. Ans.
3.—To find the Space through which a Body will fall in any given time.
Multiply the square of the time, in seconds, by 161⁄12, and it will give the space in feet.
Example. Required the space fallen through in seven seconds.
161⁄12 × 7² = 7881⁄12 feet. Ans.
4.—To find the Time which a Body will occupy in falling through a given space.
Divide the square root of the space fallen through by 4, and the quotient will be the time in which it was falling.
Example. Required the time a body will take in falling through 402.08 feet of space.
√402·08 = 20·049, and 20·049 ÷ 4 = 5·012. Ans.
5.—The Velocity being given, to find the Space fallen through.
Divide the velocity by 8, and the square of the quotient will be the distance fallen through to acquire that velocity.
Example. If the velocity of a cannon ball be 660 feet per second, from what height must a body fall to acquire the same velocity?
660 ÷ 8 = 82·5² = 6806·25 feet. Ans.
6.—To find the Time, the Velocity per second being given.
Divide the given velocity by 8, and one-fourth part of the quotient will be the answer.
Example. How long must a bullet be falling, to acquire a velocity of 480 feet per second?
480 ÷ 8 = 60 ÷ 4 = 15 seconds. Ans.