A jet aircraft is flying horizontally at a constant altitude of 4000\,m and a constant speed of 250\,m\,s−1 along a straight path that passes directly over an observer on the ground. Let θ(t) be the angle of elevation of the jet as seen from the observer. Find the rate of change of θ when the horizontal ground distance between the jet and the observer is 3000\,m.
a. Provide a complete calculation of dtdθ at the specified instant, including any formulas you use, intermediate steps, and the final numerical answer with correct units.