A vertical tower AO of height h metres stands with its base A on horizontal ground. A stone is projected horizontally from the top O of the tower with speed V ms¹. The stone moves in a vertical plane under gravity where the acceleration due to gravity is g ms ². At time t seconds its position vector relative to O is r(t) = Vt i-gt² j. The stone hits the ground at an angle of 45° to the horizontal. What is the time of impact? (A) (B) (C) (D) V 2g V g 2V g 4V g seconds seconds seconds seconds

Time for some rocket science (or AV-tech science?)! Let's go to Mars (on TV)! A television camera is positioned 4000 m from the base of the Mars Explorer rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 600 m/s when it has risen 3000 m. (a) How fast is the distance from the television camera to the rocket changing at that moment? (b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment? (a) (b) m/s radians/s