Answer:
We can use the kinematic equation for vertical motion:
y = v0*t + (1/2)at^2
where y is the height, v0 is the initial velocity (in the vertical direction), a is the acceleration (due to gravity), and t is the time.
At the highest point of the stone's trajectory, its vertical velocity will be zero, so we can use the initial velocity as 0 and the acceleration as -9.8 m/s^2.
Using the height of the building as the initial height, we get:
-50.0 m = 0*t + (1/2)(-9.8 m/s^2)*t^2
Simplifying and solving for t, we get:
t = sqrt(2*(-50.0 m) / -9.8 m/s^2) = 3.19 seconds
Therefore, it will take approximately 3.19 seconds for the stone to reach the level ground below. Note that the horizontal speed of the stone does not affect the time it takes to fall vertically.