Final answer:
To calculate the horizontal distance the ball will travel, we first determine the time it takes to fall the 10 m height, then use the initial horizontal velocity to find the distance. The time to fall is approximately 1.43 seconds, and the horizontal distance traveled is thus around 143 m, so the nearest answer choice is 200 m (D).
Step-by-step explanation:
The question concerns finding the horizontal distance a ball will travel when kicked horizontally from the top of a structure before hitting the ground. We can use the equations of motion in two dimensions to solve this.
Since the ball is kicked horizontally, its initial vertical velocity is 0 m/s. To find out how long it takes for the ball to reach the ground, we can use the formula h = (1/2)gt², where h is the height, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.
For a 10 m tall structure:
10 = (1/2)(9.8)t² => t² = 10 / 4.9 => t = √(2.04) => t ≈ 1.43 s
Using the time, we can calculate the horizontal distance using the horizontal velocity, v = d/t.
So, d = v*t = 100 m/s * 1.43 s = 143 m
The closest answer choice to 143 m is D) 200 m.