If the speed of a roller coaster at the bottom of a hill is 20.0 m/s , what is the tallest hill the coaster can climb, assuming no friction losses ?

20.4 meters

Explanation:

KE = 1/2 m v^2 = mgh = PE (convert all kinetic energy to potential energy, because at the highest point the coaster can climb, it will be stopped!)

=> h = (1/2 m v^2) / (mg) = v^2/(2*g) = (20 m/s)^2 / (2*9.8 m/s^2) = 20.4 m