An aircraft \(P\) takes off at \(A\) with a velocity \(v_{0}\) of \(250 \mathrm{~km} / \mathrm{h}\) and climbs in the vertical \(y^{\prime}-z^{\prime}\) plane at the constant \(15^{\circ}\) angle with an acceleration along its flight path of \(0.8 \mathrm{~m} / \mathrm{s}^{2}\). Flight progress is monitored by radar at point \(O\).

(a) Resolve the velocity of \(P\) into cylindrical-coordinate components 60 seconds after takeoff and find \(\dot{r}, \dot{\theta}\), and \(\dot{z}\) for that instant.

(b) Resolve the velocity of the aircraft \(P\) into sphericalcoordinate components 60 seconds after takeoff and find \(\dot{R}, \dot{\theta}\), and \(\dot{\phi}\) for that instant.

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3 km A X R 15 P