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Calculate distance fallen when object is already in motion when time begins

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The question posed is:

A person looking out of a window of a tall building sees a bucket fly past the window at 30 m/s, then hears the bucket hit the ground 8 seconds later. At what altitude is the observer located? Assume negligible air resistance and speed of sound at 340 m/s.

The problem I am having is that the sound takes an unknown time to arrive at the observer after hitting the ground.

(upload doesn't seem to be working so here is link:)

http://postimg.org/image/ezfnkds9j/

Using the common kinematic equations and substitution, I have a couple of formulas:

What are the steps using my equation, if correct? I haven't managed to do it.

Or, how do I solve it after setting equation#1 equal to velocity * (total time - time for sound to reach observer)?

I have found various equations for solving similar penny/stone in the well problems , but they all assume a starting velocity of zero.

As an additional question, what area of algebra should I practice here, in order to solve equations like this?

Thanks!

asked Apr 20, 2016 in Others by Dale
edited Apr 20, 2016

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