To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. How high is the building if the splash is seen 6.7 seconds after the stone is dropped? Use the position function for free-falling objects given below. (Round your answer to one decimal place.)
To estimate the height of the building, we can use the position function for free-falling objects. The position function is given by:
h(t) = -16t^2 + vt + h
Where:
- h(t) represents the height of the object at time t.
- t represents the time in seconds.
- v represents the initial velocity of the object (in this case, the stone) in feet per second.
- h represents the initial height of the object (in this case, the top of the building) in feet.
In this case, the stone is dropped, so its initial velocity is 0 ft/s. Therefore, the position function simplifies to:
h(t) = -16t^2 + h
To find the height of the building, we need to determine the value of h. We know that the splash of the stone is seen 6.7 seconds after it is dropped. So, we substitute t = 6.7 into the position function:
h(6.7) = -16(6.7)^2 + h
Simplifying this equation will give us the height of the building.
To estimate the height of the building, we can use the position function for free-falling objects. The position function is given by:
h(t) = -16t^2 + v0t + h0
where:
h(t) is the height of the object at time t
v0 is the initial velocity of the object (which is 0 in this case because it is just dropped)
h0 is the initial height of the object (the height of the building)
Since the stone is dropped, the initial velocity (v0) is 0. Therefore, the position function simplifies to:
h(t) = -16t^2 + h0
We are given that the splash is seen 6.7 seconds after the stone is dropped, so we can substitute t = 6.7 into the position function:
h(6.7) = -16(6.7)^2 + h0
To solve for h0 (the height of the building), we need to know the value of h(6.7). Unfortunately, that information is not provided. So, without knowing the value of h(6.7), we cannot determine the height of the building.
The position function for a free fall from rest is:
x(t)=(1/2)gt²
In metric units (x in metres, t in seconds),
x(t)=(1/2)*(-9.8)t²
=(1/2)(-9.8)6.7²
=-220 m approx.