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278- mechanics.
Example.
A fly-wheel has a rim speed of 48 feet per second. From
what height must a body drop to acquire the same velocity ?
Solution :
A = ."L = »L = 230
± = 85.78 feet.
2 g 64.4 644
Time.
Rule.
Divide the space by 16.1, and the square root of the
quotient is the time ; or, divide given velocity by 32.2, and the
quotient is the time.
Example.
How long a time does it take before a body in a free fall
acquires a velocity of 100 feet per second ?
Solution
:
t — ^L.— 152 = 3.1 seconds.
g 32.2
Distance a Body Drops During the Last Second.
The space through which a body will drop in the last
second is equal to the final velocity minus half of acceleration
due to gravity. Therefore, this space is found by the formula:
x — v — y
2 g = g{t — y
2 )
x = Space in feet which the body drops the last second of
the fall.
/ == Time in seconds.
v = Final velocity.
g = Acceleration of gravity = 32.2 feet.
h = Height of fall in feet.
Example.
40 feet
per
Solution
A body has in a free fall obtained a final velocity of
second. What space did it drop the last second ?
x = v — V
2 g — 40 — ^-2
= 40 — 16.1 = 23.9 feet.
Example.
A body was falling four seconds. How many feet did it
drop the last second ?
Solution :
x — g{t — y
2 ) = 32.2 X (4 — y
2 ) = 32.2 X 3.5 = 112.7 feet.
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