How long does it take to hit?

Let the velocity of the stone just before hitting the plane be $v$ . Since the stone hits the plane normally, the horizontal component of this velocity is $v\cos 30\degree=\dfrac{v√3}{2}$ . Since there is no acceleration in the horizontal direction, $\dfrac{v√3}{2}=179.315\cos 45\degree=\dfrac{179.315}{√2}$ . Similarly, for the vertical component of velocity, we can write $-v\sin 30\degree=179.315\sin 45\degree-gt=\dfrac{179.315}{\sqrt 2}-10t$ , or $\dfrac{v}{2}=10t-\dfrac{179.315}{\sqrt 2}$ . From these we get $t=\dfrac{(√3+1)\times 179.315}{10√6}\approx {19.999989}$ . Hence the answer is $\boxed {20}$