If the initial velocity is doubled, how does the range of a projectile change, assuming no air resistance?

Quadruples. If the initial velocity of a projectile is doubled while maintaining the same launch angle and in the absence of air resistance, the range of the projectile will increase by a factor of four, or quadruple. This result can be understood by examining the equation for the range of a projectile, which is directly proportional to the square of the initial velocity (R ∝ v^2). By doubling the initial velocity, the kinetic energy of the projectile increases fourfold, leading to a significantly greater range. This principle is an important aspect of projectile motion and can be applied to various scenarios, from sports to aerospace engineering, where maximizing the range of a projectile or an object's flight is desired.