1. A space-ship is heading towards a planet, following the trajectory, r(t) = (Ae-t² cos(3t), √2Ae-t² sin(3t), -Ae-t² cos(3t)), where A 50,000km and the time is given in hours. (a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does the ship reach the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. = (b) To 4 significant figures and including units, what are the velocity and speed of the space-ship when it reaches the planet?

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