Question

Two identical arrows, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant “frictional” force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Short answer

The faster arrow will cover four times the distance covered by the slower arrow.

Step-by-step solution

Understanding kinetic energy

In this problem, use the relation of the kinetic energy of the arrow with the speed and mass of the arrow.

When the speed of the arrow becomes twice, the kinetic energy will multiply by a factor of four.

Evaluation of the penetration of the faster arrow as compared to the slower arrow

The masses of both arrows are the same, but one of them is twice as fast as the other. Since the faster arrow’s kinetic energy is four times the kinetic energy of the slower arrow, so the work done on the faster arrow will also be four times.

Also, the work done is directly proportional to the distance. Hence, the faster arrow covers four times the distance covered by the slower arrow.