An amusement park commissions your company to design a roller coaster. Your company specializes in an approach in which the cars are accelerated on a horizontal section of track by magnetic motors rather than being hauled up to the top of a hill and released. The park officials would like the riders to be accelerated via your horizontal design and then sent straight up a vertical length of track \(66.4 \mathrm{~m}\) tall. (After the cars pass this high point, the ride is the regular ups and downs of a conventional roller coaster.) Your calculations tell you that 212 motors will get the loaded cars up to the necessary speed at an acceleration of \(0.85 \mathrm{~g}\), but you wonder whether or not the park has enough horizontal distance available for the acceleration device.