Final answer:
The maximum height h that a ball reaches when projected vertically upwards depends on its initial velocity u and the acceleration due to gravity g. The correct formula is h = u² / (2g). Additional information about the initial velocity is required to solve for h using this formula.
Step-by-step explanation:
Calculating Maximum Height of a Projectile
To determine the maximum height (h) that a ball reaches when it is projected vertically upwards with an initial velocity of u, we must consider the acceleration due to gravity (g). Typically, the equation h = u² / (2g) is used, where h is the maximum height, u is the initial vertical velocity, and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth's surface). It is important to note that the maximum height is achieved when the projectile's velocity reaches zero.
In this scenario, we need more information to calculate h accurately, either the value of initial velocity u or additional context to be able to determine the height with the provided equation h = 2g, which appears incorrect as it does not account for the initial velocity. For projectiles, it is also assumed that up is positive, hence the initial velocity is also positive, while the acceleration due to gravity is negative.
A real-world example is the launching of fireworks, which reach their maximum height before exploding. Without air resistance, any projectile with a specific initial vertical velocity will reach the same maximum height. However, with air resistance, the initial velocity needs to be greater to achieve the same height.