Originally Posted by **shaojie2k**

This is a qns from GCSE A level.....Appreciate your help !

In the diagram, O and A are fixed points 1000m apart on horizontal ground. The point B is vertically above A, and represents a balloon which is ascending at a steady rate of 2m/s. The balloon is being observed from a moving point P on the line OA. At time t=0, the balloon is at A and the observer is at O. The observation point P moves towards A with steady speed 6m/s. At time t, the angle APB is θ radians. Show that dθ/dt = 500/(t^2+(500-3t)^2).