The scenario i am interested in is similar to that of accelerating up an inclined plane, however all the problems I've seen are flat inclines (straight lines at an angle). My question is; say that a skateboarder wants to jump a ramp and must clear a 25 foot horizontal distance and land on a second downward ramp that is one foot higher than the original.
I am very familiar with kinematic equations and if this were a simple incline plane problem it would be very simple. However, say the takeoff ramp is not flat, but has a curve in it (semicircular). How would you calculate the amount of speed necessary to clear the path? Surely you would have to take into account the exact takeoff angle at the end of the ramp along with the initial velocity of the free fall jump, but on the show 'silicon valley' the engineers mention that a different method is required to properly calculate takeoff velocity. Please provide an example including friction (say the person weighs 90 kg and the friction factor of the bike tire to the dirt is 0.7 and the tire to the ramp is 0.5), showing what makes it different than a regular flat ramp.