Elasticity was first investigated by English physicist Robert Hooke, who developed a series of principles known as Hooke's Law. According to Hooke's Law, the stretch of an elastic material will be proportional to the effort applied. Because energy is conserved, stretching a slingshot twice as far should result in a projectile traveling twice as fast.
The speed of the projectile is a component of its kinetic energy:
`KE = 1/2 mv^2`
where m is the mass of the projectile and v is its velocity. Since the velocity is squared, doubling the speed of the projectile will result in it having four times the kinetic energy. When the projectile hits something it transfers its energy to whatever it hit, which results in damage. Twice the stretch =twice the speed = four times the kinetic energy = four times the damage.