A man  is running  with constant  speed  of $\text{v=10}\sqrt{\text{5}}\text{m/s}$ on a horizontal track  of radius  R=20m as  shown  in figure. At position  A,  man launches  a stone  in space  (without  changing  his own  speed) so that he  can catch  stone at B (diametrically  opposite to A)  The speed  of launch is approximately   4 Km/sec Then find  the value  of K (take ${\text{π}}^{\text{2}}{\text{=10m/s}}^{\text{2}}$)