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What you really need to find out is how fast the projectile will leave the arrow. The projectile's MASS (not its weight) and the force with which the bow pushes it can help you calculate the acceleration (using Newton's Second Law), but that's really insufficient information - you also need to know for how long the bow pushes the projectile, using the given force.

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Q: How can I find the maximum distance a bow can shoot a projectile based on the projectile's weight and draw weight of the bow?
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