Final answer:
To determine the horizontal distance the ball lands from the base of the building, we can use the principles of projectile motion. By calculating the time of flight and then using it to find the horizontal distance, we can determine that the ball will land approximately 30.14 m from the base of the building.
Step-by-step explanation:
To answer this question, we can use the principles of projectile motion. Since the ball is thrown horizontally, its initial vertical velocity is 0 m/s. The only force acting on it is gravity, causing it to accelerate downward at 9.8 m/s². We can use the formula:
d = v0t + 0.5at²
where d is the horizontal distance, v0 is the initial horizontal velocity, a is the acceleration due to gravity, and t is the time of flight. We can set d as the unknown and solve for t. Given that the initial horizontal velocity is 13.7 m/s and the height of the building is 27.3 m, we can calculate the time of flight using the formula:
t = √(2h / g)
t = √(2 * 27.3 / 9.8) = 2.2 s
Then, we can calculate the horizontal distance using the formula:
d = v0t
d = 13.7 * 2.2 = 30.14 m
Therefore, the ball will land approximately 30.14 m from the base of the building.