Question $3[10$ points$]$ Among the three following launch sites, which one would give the maximum boost from Earth$$s rotation for a launch due east? Why is it advantageous to have maximum boost from Earth$$s rotation for a launch due east? Show your calculations for each launch site. Use $6371$ km for Earth$$s radius. $($a$)$ SpaceX Starbase Spaceport, Texas $(25\mathrm{.}996$N $97\mathrm{.}154$W$)$

$($b$)$ Vikram Sarabhai Space Centre $($VSSC$),$ India $(8\mathrm{.}5314$N $76\mathrm{.}8690$E$)$

$($c$)$ Jiuquan Satellite Launch Center $($JSLC$),$ China $(40\mathrm{.}96056$N $100\mathrm{.}29833$E$)$