Answer to Question #7215 in Calculus for Haley Heinemann

Question

Robin is running around on the inside of a bowl-like surface, z = x^2 + y^2 , with distance measured in meters. It is noon, the sun is directly overhead, and the birds are silent. All of a sudden, much to her horror, she realizes someone has chopped off the bowl at a height of 3 meters. But she is too close to the edge and running too fast, so she flies up off the edge of the bowl at a speed of 5 meters per second. As she flies up off the edge, she looks down at the ground below (the xy-plane) and sees her shadow. She observes that it is in the first quadrant, has x-coordinate 1, and it is heading directly towards a house with coordinates (2,4). Realizing she has no parachute, she wonders (of course) how long it will be before she hits the ground and where she will land. Set her mind at ease by answering these two questions for her. Ignore air resistance.