Estimate height using position-function

Question

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 6.9 seconds after the stone is dropped?

Use the position function for free-falling objects given below. (Round to one decimal place.)

s(t) = –4.9t² + v₀t + s₀

(height in meters)

Would greatly appreciate some guidance on this.

Answer 1

233.9 meters high

4.9(6.9)^2 = 233.9

s= 0 = -4.9(6.9)^2 + 0(6.9) = so

so = 233.9

Answer 2

We can start by simplifying the v₀t part of our equation to 0, because the initial velocity as its "dropped" is 0 m/s and accelerates due to gravity. Therefore our simplified equation looks like:

s(t) = -4.9t² + s₀

at time t = 6.9, our s(t) should equal 0 since that is when it hits the ground. We can plug in these values to solve for the initial position s₀:

0 = -4.9(6.9)² + s₀

Solve for s₀:

s₀ = 4.9(6.9)² = 233.3 m