Final answer:
To estimate the height of the building, we can use the position function for free falling objects. By substituting the given time of 5.8 seconds into the position function, we can calculate the height of the building to be approximately 57.6 meters.
Step-by-step explanation:
To estimate the height of the building, we can use the position function for free falling objects. The position function is given as s(t) = -4.9t^2 + v₀t + s₀, where t is the time in seconds, v₀ is the initial velocity in meters per second, and s₀ is the initial position in meters.
In this case, the stone is dropped from the top of the building, so the initial velocity is 0 m/s. The initial position is the height of the building, which we want to find.
Since the stone hits the water 5.8 seconds after it is dropped, we can substitute t = 5.8 into the position function. We get:
s(5.8) = -4.9(5.8)^2 + 0(5.8) + s₀
s(5.8) = -4.9(33.64) + s₀
s(5.8) = -165.236 + s₀
Since the stone is dropped from the top of the building, the initial position s₀ is equal to the height of the building. Plugging in the known values, we get:
h = -165.236 + s₀
s₀ = h + 165.236
Therefore, the height of the building is given by:
h = s(5.8) + 165.236
Calculating this value gives us:
h = -4.9(5.8)^2 + 0(5.8) + 165.236
h = -4.9(33.64) + 165.236
h ≈ 57.6 meters