An archer pulls back the string of a bow to release an arrow at a target. which kind of potential energy is transformed to cause the motion of the arrow?

It is elastic energy

I think the kind of potential energy that is transformed to cause the motion of the arrow would be elastic energy. Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume or shape. 

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100 pounds is 100 pounds no matter the object or item being weighed