Doubling the initial velocity of a projectile while keeping all other parameters the same, the height reached by the projectile increases by:

Explanation

When a projectile is launched, the maximum height it reaches is directly related to the square of its initial vertical velocity. The formula for maximum height (H) is given by H = (v0y2)/(2g), where v0y is the initial vertical velocity and g is the acceleration due to gravity. When the initial velocity is doubled (v0y becomes 2v0y), the new height becomes H' = (2v0y)2/(2g) = 4(v0y2)/(2g) = 4H. Thus, the height increases by a factor of four. The other options (two times, three times, and remains the same) do not account for the quadratic relationship between velocity and height, which is why they are incorrect.