Two identical arrows,one with twice the speed of the other,are fired into a hay bale.The faster arrow will penetrate

Question

Quizplus · Accepted Answer

The kinetic energy of an object is given by 1/2mv^2, where m is the mass of the object and v is its velocity. Since the arrows are identical, they have the same mass. However, the faster arrow has twice the velocity of the slower arrow, so it has four times the kinetic energy (1/2m(2v)^2 = 1/2m(4v^2)). When the arrows hit the hay bale, this extra kinetic energy is transferred into work done on the bale, causing the faster arrow to penetrate further. Since the kinetic energy is proportional to the square of the velocity, the faster arrow will penetrate four times further than the slower arrow (choice C).

Two Identical Arrows,one with Twice the Speed of the Other,are