Final answer:
The height of the balcony, calculated using the formula for distance fallen under constant acceleration, is 35.621 meters, which does not match any of the provided multiple-choice options. The question may contain a typo or an error.
Step-by-step explanation:
To determine how tall the balcony is, we need to consider only the vertical motion of the soccer ball because the initial horizontal velocity does not affect the vertical drop. While the ball falls, gravity accelerates it downwards at a rate of 9.8 m/s2, which is the acceleration due to gravity. The formula to calculate the distance fallen under constant acceleration is d = 0.5 * g * t2 where d is the distance fallen, g is the acceleration due to gravity, and t is the time the ball has been falling.
Plugging in the values we get:
- d = 0.5 * 9.8 m/s2 * (2.7 s)2
- d = 0.5 * 9.8 m/s2 * 7.29 s2
- d = 0.5 * 71.242 m/s2
- d = 35.621 m
Since the calculated distance is not one of the options provided and because the question likely contains a typo, I am unable to provide an accurate answer to the given multiple-choice question.