Having trouble solving a problem regarding the bouncing ball series in terms of the time needed for the ball to stop bouncing.

We are to first find an equation for time (t) in terms of height (h)

I had used the formula h=g(gravity) * (1/2)t^2, gravity being in English units of measurement so approximately 32 ft/sec

That came to t = (1/4) sqrt(h)

We then are given height h = 12 ft and are told to compute how long it will take for the ball to stop bouncing given the ball bounces back up 3/4 of the height of the previous height.

Using h = 12 and r(common ratio) = 3/4, I then used the formula S = a / (1 - r) and came up with 2sqrt(3) seconds, approximately 3.464 seconds.

I didn't feel all to confident in my methods to begin with but based upon a short conversation with classmates, I am nearly certain I have gone about this incorrectly.

Any pointers towards the right way to go about solving this would be much appreciated and any detailed breakdown to accompany it would be fantastic.