2022 HCI P1 Q11

Sam tests his kite at an open area, and he wants to fly his kite at a fixed vertical height of \(30\)m above the horizontal ground as shown in the diagram below. The wind blows the kite horizontally from point \(P\) to \(Q\) with a speed of \(2.4\)m/s. The string attached to the kite is temporarily tied to the point \(O\) on the horizontal ground. Find the rate at which the angle made between the string and the horizontal, \(\theta \) measured in radians, is decreasing at the instant when Sam lets out \(10\sqrt{10}\)m of his string.[4]