Final Answer:
The height of the building is approximately 24.4 meters.
Step-by-step explanation:
Identify the relevant equations:
The horizontal and vertical motions of the rock can be described by the following independent equations:
Horizontal Motion:
x = v_x * t
where:
x is the horizontal distance traveled
v_x is the initial horizontal velocity (10.0 m/s * cos(30°))
t is the time of flight
Vertical Motion:
y = v_y * t - 0.5 * g * t^2
where:
y is the vertical displacement (height of the building)
v_y is the initial vertical velocity (10.0 m/s * sin(30°))
g is the acceleration due to gravity (9.81 m/s²)
Solve for the time of flight:
We are given the horizontal distance traveled (x = 43.0 m). Since we know v_x, we can solve for the time of flight using the horizontal motion equation:
43.0 m = (10.0 m/s * cos(30°)) * t
t ≈ 5.09 s
Solve for the height of the building:
We are given the time of flight (t) and the initial vertical velocity (v_y). We can solve for the height of the building (y) using the vertical motion equation:
y = (10.0 m/s * sin(30°)) * 5.09 s - 0.5 * 9.81 m/s² * (5.09 s)^2
y ≈ 24.4 m
Therefore, the height of the building is approximately 24.4 meters.