A particle of mass \( 100 \, \text{g} \) is projected at time \( t = 0 \) with a speed \( 20 \, \text{m} \, \text{s}^{-1} \) at an angle \( 45^\circ \) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \( t = 2 \, \text{s} \) is found to be \( \sqrt{K} \, \text{kg} \, \text{m}^2 / \text{s} \). The value of \( K \) is ________. (Take \( g = 10 \, \text{m} \, \text{s}^{-2} \)).
