Final answer:
The physics question pertains to calculating the maximum height a ball reaches when kicked with an initial vertical velocity. The maximum height is found using the equation h = v^2 / (2g). The provided example used a vertical velocity of 12 m/s, resulting in a height of approximately 7.34 meters.
Step-by-step explanation:
The question addresses the concept of projectile motion in physics, specifically the maximum height a ball can reach when kicked with a given initial velocity. When a ball is kicked with an initial vertical velocity, it will rise to a height where the vertical component of its velocity is reduced to zero due to the acceleration due to gravity before falling back down.
Using the formula for the maximum height (h) reached by a projectile under gravity is h = v2 / (2g), where v is the initial vertical velocity and g is the acceleration due to gravity (approximately 9.81 m/s2).
Considering the question provided where a ball is kicked with an initial vertical velocity of 12 m/s, and applying the formula:
h = 122 / (2 * 9.81) = 144 / 19.62 = 7.34 meters (approx)
If we consider the options given in the student's question, option C) 5.1 meters appears to be the closest to the calculated height of 7.34 meters. However, since the initial velocity provided in the student's question is 8.5 meters (this seems to be an incomplete statement and must be in m/s), there seems to be some misunderstanding because the exact value of the vertical component of the velocity is required to calculate the maximum height. Assuming the given value was intended to be 8.5 m/s (vertical velocity), the calculation would give a different maximum height.
Therefore answer is C) 5.1 meters.