I was a little surprised to find pmb's value differerent from 93.9 though the approach is nice and i couldn't spot anything wrong. So i tried to calculate using the difference in time and used the following equations.

$\displaystyle H = \frac{1}{2}gt^2$

$\displaystyle H-38 = \frac{1}{2}g(t-1)^2 + 38 $.

Solving the above i ended up with t = 4.377 secs giving me H = 93.898 as before.

I finally found that the problem was in this step

as g should multiply 1/2 also here.

With this, the answer works out to be the same i.e. 93.90