## Physics: Principles with Applications (7th Edition)

Kinetic energy is $\frac{1}{2}mv^{2}$. The faster arrow has identical mass, and twice the speed, so it has four times the kinetic energy. Four times as much (negative) work must be done on it to stop it. We’re told that the force on each arrows is the same and constant, so the faster arrow travels 4 times the distance into the hay, compared to the slower arrow.