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MECHANICS. 279
TABLE No. 35—Time, Velocity and Height.
jr= 32.161 Feet.
-T- -
c , 1 Velocity in Feet at
Tune in Seconds. ,
the End £f the Time
Height of Fall in
Feet.
Distance in Feet that
the Body Drops in
the Last Second.
1
2
3
4
5
32.161
64.322
96.483
128.644
160.805
16.08
64.32
144.72
257.28
402.00
16.08
48.24
80.40
112.56
144.72
Upward Motion.
A body thrown perpendicularly upward with a certain
velocity will continue the upward movement until it reaches the
same height from which it would have to fall in order to get a
final velocity equal to the starting velocity. Therefore, a body
projected upward with a given velocity will return again with
the same velocity. This is theoretical in a vacuum, but actually
the body neither continues to the theoretical height nor returns
with a final velocity equal to the starting velocity, because the
air will always offer considerable resistance. The greater the
weight of a body, in proportion to its volume, the nearer the
velocity, when it returns, will be equal to its starting velocity.
Example.
A body is projected upward with a velocity of 45 feet per
second. How high will it go before it stops and commences to
drop again, the resistance of the air not being considered ?
The solution of this problem is simply to find the theoretical
height from which a body must drop to attain a final velocity of
45 feet, which is solved by the formula,
452
6474
2025
64.4
11.286 feet.
Body Projected at an Angle.
If a body is projected in the direction of the line d e (see
Fig. 1), with an initial velocity per second equal to the distance
from d to 1, no force acting after the body is started, it will con-
tinue to move at constant velocity in a straight line indefinitely ;
at the end of the first second it would be at 1, at the end of
two seconds it would be at 2, at the end of the third second at 3,
at the end of the fourth second at 4, etc.; but, on account of the
force of gravity, the motion will be entirely different. The
force of gravity acts on this body exactly as if it was falling in
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