Time flies when you're doing physics!

Classical Mechanics Level pending

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?

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