A person 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)