Time flies when you're doing physics!

Timothy, a curious boy, was eager to explore the phenomenon of time flying. To his dismay, upon throwing his standard analogue clock out of his apartment window $100m$ above the ground, it merely accelerated towards the ground at the standard $10ms^{-2}$ . Assuming that Timothy projected his clock horizontally and ignoring air resistance, what angle to the nearest multiple of 6 degrees would the second hand have moved around the clock's centre from the time of projection to the time at which the clock hit the ground?