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. The splash is seen 5.6 seconds after the stone is dropped. What is the height of the building? Use the position function s(t) = 4.9t² + v_0 t + s_0 for free falling objects.

Answer 1

Answer:

The height of the building is 153.664 meter.

Step-by-step explanation:

Consider the provided function.

$s(t) = 4.9t^2 + v_0 t + s_0$

Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.

It is given that the splash is seen 5.6 seconds after the stone is dropped.

That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.

Substitute respective values in the above function.

$0 = 4.9(5.6)^2 +5.6(0)+ s_0$

$0 = 4.9(31.36)+ s_0$

$s_0=-153.664$

As height can't be a negative number so the value of s₀ is 153.664.

Hence, the height of the building is 153.664 meter.