Imagine that you are working as a roller coaster designer. You want to build a record- breaking coaster that goes 70 m/sec at the bottom of the first hill. you estimate that the efficiency of the tracks and cars you are using is 90%. How high must the first hill be?

Arope has one end tied to a vertical support. you hold the other end so that the rope is horizontal. if you move the end of the rope back and forth with a frequency of 4 hz, the transverse wave you produce has a wavelength of 0.5 m. what is the speed of the wave in the rope?