Your aunt owns an amusement park, and she wants you to add a circular loop to an existing roller-coaster ride. The first hill for the existing roller coaster is \(55 \mathrm{~m}\) tall, and your aunt wants you to build, right after this hill, the tallest loop possible without having the cars fall out of the track or the passengers fall out of the cars. You think for a minute and realize what the minimum speed at the top of the loop has to be, and this gives you what you need to design the loop.