1. The problem statement, all variables and given/known data A roller coaster starts at the top of hill that is 10 m high. If it is to barely make it to the top of a second hill that is 20 m high, how fast must the initial speed of the roller coaster be? Assume that the roller coaster is frictionless. 2. Relevant equations KE = 0.5mv^2 PE = mgh 3. The attempt at a solution mgh=0.5mv^2 gh = 0.5v^2 v = sqrt(2gh) v = sqrt(2*9.81*20) v = 20 m/s needed at bottom of second hill. mgh=0.5mv^2 gh = 0.5v^2 v = sqrt(2gh) v = sqrt(2*9.81*10) v = 14 m/s at bottom of hill if initial velocity at top of first hill is 0m/s. 20 m/s - 14 m/s = 6 m/s 6 m/s is the velocity of the roller coaster at the top of the first hill. Does that look right?