76Part 1Introductiona.Howdoes the valueoftat which the heightofthe ball is at a maximum depend on theparameterg1b. Use your answer to part (a) to describe how maximum height changes as the parametergchanges.c.Use the envelope theorem to answer part (b) directly.d.Onthe Earthg=32,butthis value varies somewhat around the globe. If two locations hadgravitational constants that differed by 0.1, what would be the difference in the maximumheightofa ball tossed in the twoplaces12.6A simple way to model the constructionofan oil tanker is to start with a large rectangular sheetofsteelthat isxfeet wide and3xfeet long.Nowcut a smaller square that istfeet on a sideoutofeach cornerofthe larger sheet and fold up and weld the sidesofthe steel sheet to make a traylike structure with no top.a. Showthatthe volumeofoil that can be held by this tray is given byV=t(x-2t)(3x-2t)=3tx2-8t2X+4t3.
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