1. Callisto is Jupiter's second largest moon and the third largest moon in our solar system....

 

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1. Callisto is Jupiter's second largest moon and the third largest moon in our solar system. It's about the same size as Mercury. Let's assume that Callisto's icy surface has completely melted when an alien ship lands on a solid island on this moon. a) The surface of the island is described by z=- − ( ²² +²²) +1 in kilometers. Plot, in MATLAB, the 3D surface of the island above the water, label the axes. b) What is the maximum height and the diameter of the island, assuming that the level of the ocean is at z = 0? c) Show three level curves of the island's surface on a 2D map, starting with level z= 0. d) Landing on Callisto is hard. The alien spaceship has two options for landing: at locations (x = 2, y = 2) or (x = 1/2, y = 1/2). Which coordinates will land the ship on solid ground? e) Assuming the alien ship landed safely (choose the appropriate coordinates from part d), a lander is deployed to the ground. For better reception the lander's antenna pole has to be positioned perpendicular to the ground surface. Find the orientation of the pole, by estimating the outward surface normal vector N to the surface at that location. f) Unfortunately, the lander has faulty brakes and starts to slip. Find the 3D unit vector indicating the direction of motion from the landing position. Hint: In MATLAB quiver and contour require the use of the meshgrid first. To get a good picture, you generally need a closely spaced mesh for contour, but a sparser one for quiver. Note: Your answer to this question should include a printout of the published MATLAB script used to generate the plot. Add always comments to the code, which is part of "Mathematical arguments should be clearly and logically expressed" marking section. 1. Callisto is Jupiter's second largest moon and the third largest moon in our solar system. It's about the same size as Mercury. Let's assume that Callisto's icy surface has completely melted when an alien ship lands on a solid island on this moon. a) The surface of the island is described by z=- − ( ²² +²²) +1 in kilometers. Plot, in MATLAB, the 3D surface of the island above the water, label the axes. b) What is the maximum height and the diameter of the island, assuming that the level of the ocean is at z = 0? c) Show three level curves of the island's surface on a 2D map, starting with level z= 0. d) Landing on Callisto is hard. The alien spaceship has two options for landing: at locations (x = 2, y = 2) or (x = 1/2, y = 1/2). Which coordinates will land the ship on solid ground? e) Assuming the alien ship landed safely (choose the appropriate coordinates from part d), a lander is deployed to the ground. For better reception the lander's antenna pole has to be positioned perpendicular to the ground surface. Find the orientation of the pole, by estimating the outward surface normal vector N to the surface at that location. f) Unfortunately, the lander has faulty brakes and starts to slip. Find the 3D unit vector indicating the direction of motion from the landing position. Hint: In MATLAB quiver and contour require the use of the meshgrid first. To get a good picture, you generally need a closely spaced mesh for contour, but a sparser one for quiver. Note: Your answer to this question should include a printout of the published MATLAB script used to generate the plot. Add always comments to the code, which is part of "Mathematical arguments should be clearly and logically expressed" marking section.

Answer rating: 100% (QA)

a To plot the 3D surface of the island we can use the surf function in MATLAB The equation of the surface is given by z x2 y2 1 We can define a range ... View the full answer