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28o MECHANICS.
a vertical line. At the end of the first second the force of
gravity has caused this moving body to drop 16.1 feet out of its
path; therefore, instead of being at 1 at the end of the first
second, it is at a point 16.1 feet vertically under 1 ; instead of
being at 2 at the end of two seconds, it is at a point 2 X 2 X
16.1 = 64.4 feet vertically below 2; instead of being at 3 at the
end of the third second, it is at a point 3 X 3 X 16,1 = 144.0
feet vertically below 3 ; and instead of being at 4 at the end of
the fourth second, H is at a point 4 X 4 X 16.1 = 257.6 feet
vertically below 4, etc.
Fig. 1.
When a body is projected in a vertical upward direction
with an initial velocity of v feet per second, it proceeds to a
height -; therefore, when projected at an angle, a (see Fig.
1), with a velocity of v feet per second, it will proceed to the
, . , v2
sin.2
a
height
YJ~~
When a body is projected in a vertical upward dirction with
a velocity of v feet per second, the time for ascent is - and the
time for descent is equal to the time for ascent ; therefore,
the total time will be 2 ; but when the body is projected
upward at an angle of a degrees, the total time for ascent and
2 v sin. a
descent will be
S
The horizontal distance, or the range from d\a ;/. will be
equal to the velocity’ in feet per second multiplied by the total
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