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mechanics. 283
Example 3.
A nozzle on a hose is placed at an angle of 38° to
#
the
horizontal line and is spouting water a distance of 40 feet in a
horizontal direction. What is, theoretically, the velocity of the
water when leaving the nozzle ?
Solution
:
b g
sin. 2 a
v — /40 X 32.2
sin. 76
ft
— J40 x 32- 2 — 36.4 feet per second.
> 0.9703
Note.—In Example 2 we multiply by sine of 56 degrees,
because water is leaving the nozzle at an angle of 28 degrees,
and twice 28 equals 56. In Example 3 we multiply by sine of 76
degrees, because twice 38 equals 76. See previous explanations.
The greatest possible height will be reached if the body is
thrown perpendicularly upward. The greatest possible range is
obtained if the body is thrown at an angle of 45° and will then be :
§
At an angle of 45° the horizontal range will be twice
the greatest possible height which could have been reached if
the body had been thrown perpendicularly upward. At this
angle the horizontal range is four times the height. For an
equal number of degrees over or under 45 degrees the horizontal
range will be equal ; for instance, if a body is thrown out at an
angle of 30 or 60 degrees, the horizontal distance is the same,
but the height of ascension will be much more at 60 degrees
than at 30 degrees. It is frequently useful to notice this in
practical work. For instance, water under pressure is thrown
the farthest distance in a horizontal direction from a hose when
the nozzle is held at an angle of 45 degrees to the horizontal
line. It is possible by the same pressure to throw water twice
as far in a horizontal distance as in vertical height.
Motion Down an Inclined Plane.
A ball rolling along an incline, as
a c (Fig. 2), will have the same
velocity when it gets to c as it would
have had if dropping freely from a
to b, supposing all friction to be left
out of consideration.
The average velocity will also be
half of the final velocity, and the
time used in the fall will be the distance a c (the length of the
incline), divided by the average velocity per second.
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