Roller Coasters Need Calculus Too!

Using the specifications of the given launch roller coaster, we were able to determine the position vector of the roller coaster as a function of time. After determining the position function, we took the derivative of this function to calculate the velocity of the coaster as a function of time. From this calculated velocity vector, we were able to determine the time required for the coaster to reach its maximum height. We substitute this time value back into the position function to determine the maximum height the launch roller coaster can obtain.