Aperson does 100 joules of work in pulling back the string of a bow. what will be the initial speed of a 0.5 kg arrow when it is fired from the bow?

If all the energy she put into bending the bow is completely
transmitted to the arrow, then the arrow has the 100 joules
of kinetic energy when it leaves the bow.

                 Kinetic energy = (1/2) (mass) (speed)²

                         100 J        = (1/2) (0.5 kg) (speed²)

Divide each side by 0.25 kg:    100 J / 0.25 kg = speed²

 [ joule ] = [ newton-meter ] = kg-m²/sec²

                                                100 kg-m²/sec² / 0.25 kg = speed²

                                                 400 m²/sec² = speed²

Take the square root of each side:     speed = √400 m/s

                                                                                20 m/s

                                                                    (about 44.7 mph)                                           

The speed was not exceeded so it was slow