91Ó°ÊÓ

An aircraft A flies horizontally at a constant speed \(100 \sqrt{2} \mathrm{~km} / \mathrm{h}\) relative to the air, and its position at 1300 hours is at O. A wind speed \(100 \mathrm{~km} / \mathrm{h}\) blows from the West from 1300 to 1400 hours, after which the wind speed is \(50 \mathrm{~km} / \mathrm{h}\) blowing from the North. The aircraft adjusts its heading so as to maintain a course \(45^{\circ}\) East of North at all times. Find: (i) the East and North components of the aircraft's velocity relative to the air, both before and after 1400 hours, (ii) the aircraft's distance from \(\mathrm{O}\) as a function of time \(t\) hours elapsed since 1400 hours, assuming \(t>0\).