use to postion function s(t) = -4.9t^2 + vt + s for free-falling objects
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 6.8 seconds after the stone is dropped?
s(6.8) = 0 the ground
v = initial vertical velocity which is zero (dropped not thrown)
0 = -4.9 (6.8)^2 + 0 (6.8) + h
so
h = 227 meters
To estimate the height of the building using the position function for free-falling objects, we need to determine the value of "s" at "t = 6.8 seconds". Here's how we can do that:
The position function for free-falling objects is given by:
s(t) = -4.9t^2 + vt + s
Where:
- "s(t)" represents the position of the object at time "t", relative to a point of reference (usually the ground)
- "t" represents the time in seconds
- "v" represents the initial velocity of the object (in this case, the stone) when it is dropped
- "s" represents the initial position of the object (in this case, the height of the building from which the stone is dropped)
To find the height of the building, we need to determine the value of "s" for a given time "t". In this case, we want to find the height of the building when the splash is seen, which occurs at "t = 6.8 seconds".
Substituting "t = 6.8" into the position function, we have:
s(6.8) = -4.9(6.8)^2 + v(6.8) + s
To solve this equation, we need to know the initial velocity "v" and the initial position "s" of the stone. Unfortunately, these values are not provided in the question you have asked.
If you have additional information such as the initial velocity or the initial position of the stone, please provide it so that we can calculate the height of the building accurately.