Optimization: 1) In Physics, an object thrown vertically upward will always start to descend once it reaches its maximum height

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Optimization:

1) In Physics, an object thrown vertically upward will always start to descend once it reaches its maximum height. Determine the time of ascent if the initial speed is V_o and the acceleration due to gravity is 1/2 of that of Earth's

2) The total surface area of an industrial cylindrical autoclave is to be limited to 20m². If it is constructed to maximize the volume, what should be the ratio of the height to that of the radius?

3) Based on the concept of the previous number. If someone asks you for help in constructing a cylindrical tank with a top cover area of 100 cm², accounting the minimum surface area and maximum volume, what would you recommend for its lateral area?

Can you include the whole process and what formula did you use, so that I can understand it more? Thank you so much