The Speed of the arrow
(image credit to:
http://media.basspro.com/images/articles/arrow1.jpg)
It can be assumed that when the bow is
released that all of the potential energy, ½eFx , is converted to the kinetic energy of
the arrow. Using, m, for mass of the arrow and ,v, for the
initial
speed of the arrow, and kinematic equations. We arrive at:
½mv² = ½eFx soving for ,v, v= 1/(eFx/m)².
This turns out to be larger than the actual speed. This is because at the instant the arrow leaves the bowstring, parts of the bow are moving, these parts have some kinetic energy which, like the kinetic energy of the arrow, has been supplied by the potential energy stored in the bow. A rough idea of the speed of the arrow can be found by realizing that the speed of a particular part of the bow must be proportional to the arrow.
This turns out to be larger than the actual speed. This is because at the instant the arrow leaves the bowstring, parts of the bow are moving, these parts have some kinetic energy which, like the kinetic energy of the arrow, has been supplied by the potential energy stored in the bow. A rough idea of the speed of the arrow can be found by realizing that the speed of a particular part of the bow must be proportional to the arrow.
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