Here's why:

* Conservation of Energy: The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.

* Potential to Kinetic: In this case, the bow's potential energy is stored due to the stretched string. When released, this potential energy is converted into kinetic energy, the energy of motion, in the arrow.

* Ideal Scenario: Assuming no energy losses due to friction, air resistance, or other factors, the total potential energy of the bow will be completely transformed into the kinetic energy of the arrow.

Therefore, if the bow has 40 J of potential energy, the arrow will ideally have 40 J of kinetic energy.