The force exerted by a certain bow on an arrow decreases linearly after the arrow is relased by the archer, starting with a value F = 275 N when the bow is fully drawn and decrasing to F = 0 as the arror leaves the bow string. The tail of the arrow moves a distance of 0.5 m as the arrow is shot. Find theh final speed of the arrow, which has a mass of `3 xx 10^(-2)kg.`

Explanation

Average force acting on the arrow, `F = (275N + 0N)/(2) = 137.5 N`
Work done by the force, W = F s = (137.5 N) (0.5 m ) = 68.75 J
It is this work which is converted into kinetic energy `((1)/(2)m upsilon^2) or the arrow, i.e., W = (1)/(2)m upsilon^2`
or `upsilon = sqrt((2W)/(m)) = sqrt((2xx68.75)/(3xx10^(-2))) = 67.7 m//s`