1. A space-ship is heading towards a planet, following the trajectory, -t r(t) = Ae¯² (5 cos(4t), 4 sin(4t), −3 sin(4t)), where A 12, 000km and the time is given in hours. (a) Ⓐ✓ The planet is centred at the origin and has a radius, rp = 3,000km. At what time does the ship reach the surface of the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. (b) As an exact expression in its simplest form, what is the velocity of the space-ship at time (in hours) t = π/2?