Final answer:
The second ball will be 4 times higher than the first ball at its apex.
Step-by-step explanation:
To determine how much higher the ball will be at its apex, we can use the concept of projectile motion and compare the heights reached by the two balls. Let's assume that the initial speed of the first ball is 'v', then the initial speed of the second ball will be '2v'.
Under the influence of gravity, the maximum height reached by a projectile depends on its initial velocity. The maximum height is given by the formula:
h = (v^2) / (2g)
where 'h' is the maximum height, 'v' is the initial velocity, and 'g' is the acceleration due to gravity.
Let's calculate the maximum height for the first ball:
h1 = (v^2) / (2g)
And the maximum height for the second ball:
h2 = ((2v)^2) / (2g)
Comparing the two heights:
h2 = 4 * h1
Therefore, the second ball will be 4 times higher than the first ball at its apex.