Final answer:
Doubling the initial velocity of a projectile while maintaining the same angle of projection quadruples the maximum height, according to the formula for maximum height in projectile motion.
Step-by-step explanation:
If the initial velocity of a projectile is doubled while keeping the angle of projection the same, the maximum height reached by it will be quadrupled. This is because the maximum height H is given by the formula H = (u²sin²θ)/(2g), where u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. Since only the initial velocity u is being doubled, and the angle θ remains the same, the vertical component of the velocity (usinθ) is also doubled, resulting in the maximum height H becoming four times greater, as the term (u²sin²θ) in the equation will increase by a factor of four (2² = 4).