THE SIMPLEST SOLUTION: Since there are no external forces ALONG THE HORIZONTAL,there is no acceleration of com along horiz. either.Hence velocity is purely vertical.Let length of rod be l
let the height of com from ground at any instant be h.
therefore sin@=2h/l (from congruency and trig.)
but h=l/2-{g*[square(t)]}/2
let t square be tsquare. finaly sin@=2h/l=2*(l/2-1/2g tsquare)/l=1-g*tsquare/l hence tsquare=l*(1-sin@)/g therefore t=root of...... hence v=0 + gt=...root(gL(1-sin@)).Simple math