Find the magnitude and bearing of the velocity of \(U\) relative to \(P\).
Find the shortest distance between \(P\) and \(U\) in the subsequent motion.
(ii) Plane \(Q\) is flying with constant velocity \(160 \mathrm {~ms} ^ { - 1 }\) in the direction which brings it as close as possible to \(U\).
Find the bearing of the direction in which \(Q\) is flying.
Find the shortest distance between \(Q\) and \(U\) in the subsequent motion.
\includegraphics[max width=\textwidth, alt={}, center]{6e3d5f5e-7ffa-4111-903d-468fb4d20192-3_771_769_262_646}
A square frame \(A B C D\) consists of four uniform rods \(A B , B C , C D , D A\), rigidly joined at \(A , B , C , D\). Each rod has mass 0.6 kg and length 1.5 m . The frame rotates freely in a vertical plane about a fixed horizontal axis passing through the mid-point \(O\) of \(A D\). At time \(t\) seconds the angle between \(A D\) and the horizontal, measured anticlockwise, is \(\theta\) radians (see diagram).
Show that the moment of inertia of the frame about the axis through \(O\) is \(3.15 \mathrm {~kg} \mathrm {~m} ^ { 2 }\).
Show that \(\frac { \mathrm { d } ^ { 2 } \theta } { \mathrm {~d} t ^ { 2 } } = - 5.6 \sin \theta\).
Deduce that the frame can make small oscillations which are approximately simple harmonic, and find the period of these oscillations.
The frame is at rest with \(A D\) horizontal. A couple of constant moment 25 Nm about the axis is then applied to the frame.
Find the angular speed of the frame when it has rotated through 1.2 radians.