Algebra Theoretical And Practical

Cover Algebra Theoretical And Practical
Algebra Theoretical And Practical
Ebenezer Bailey
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5. If the height through which a heavy body falls in different periods of time be proportional to the squares of these times, in how many seconds will a body fall through 400 feet, the space it falls through in one second being = 16*1 feet ?
Let x = the number of seconds occupied in falling through 400 feet; then 16-1 : 400 = l 2 :x 2, hence 16-lx 2 = 400, 2 _ 400 X 16-1 24- . -. X = V24-8 = + 4*9, or nearly 5 seconds.
The negative value — 4-9 implies that a heavy body thrown upwards with such
...a velocity as would make it ascend to 400 feet, would take 4-9 seconds of time to reach that height. The velocity cannot be taken in an opposite sense, but the direction of the motion can be so, and by this change a proper interpretation of the negative value is determined.
6. If the force of the earth's attraction at any point not within its surface diminish inversely as the square of its distance from the centre, at how many semi-diameters distant from the earth's centre will this force be 16 times less than at its surface?


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