The impulse momentum theorem says that the impulse on an object is equal to the change in the objects momentum. The object started at rest so it had no momentum the the impulse is equal to its final momentum
J = p2-p1 = p2-0 = p2
We know how much work the bow did on the object be multiplying the 130 Newtons of force by the .7 meters it moved under the force which is 91. The kinetic energy of an object of equal to its momentum squared divided by twice the mass
KE = (p^2)/2m
91 = (J^2)/2m in this case
so to solve for J just solve this equation with the mass of the arrow which I can't unfortunately see from your scan.
Oct 12th, 2014
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