Sometimes, people make big balloons. They may or may not be used for weather monitoring and may or may not have cameras. But they do drift into foreign airspaces. You are an engineer tasked with designing a spherical one, for 'civilian use'. The balloon should be made from a thin, strong, and non-elastic material that has a mass per unit area m=50g/m2. The payload it has to carry is 10kg. You have decided to fill it with Helium (Others who tried it with an even lighter gas didn't have too much luck due to non-fluid-mechanical reasons!) (a) (7 points) What is the radius, R0 that the balloon needs to have to be able to lift-up with the payload at sea level? The density of Helium at sea level is He=0.1785kg/m3. The density of air at sea level is Air=1.22kg/m3. Ignore the buoyancy force of the payload volume (Gameras Payloads these days are small!), but don't forget the weight of the balloon itself. (b) (7 points) As the balloon goes to higher elevations, the density of air and pressure decreases. How does the density of the helium inside the balloon change? (Hint: the balloon doesn't stretch or go floppy) (c) (8 points) We want this balloon to fly above passenger airplanes, let us say at 50,000ft. What is the radius of the balloon, R50K to reach this elevation? The MATLAB functions 'atmosisa' can be used to get air density at different elevations (in m ), and 'roots' can be used to solve cubic equations. See MATLAB documentation. (d) (8 points) Using MATLAB, plot the balloon radius for 200 values between 0 and 50000ft. You see that the curve behaves funnily as you approach 50000ft. Can you describe what is happening and why