I have solution written upto Use Matlab or Maple Solve from

I have solution written upto Use Matlab or Maple. Solve from writtin using your suggested shape,

(5) Organizing officials from the X-games hear that you have a knack for applied problems. They fly you from Cleveland to San Diego to help design the half-pipe for the skateboard competition. This year they are considering building a half-pipe which maximizes the contestants speed (assume only gravity is at work here and there is no friction or air resistance). What shape do you suggest to them? They will need justification (mathematically) and visually so you should include a plot (use Matlab or Maple). Using your suggested shape, calculate the time it takes for a contestant starting at rest at the top of the half-pipe to get to the very bottom. Also, calculate the time if the contestant starts half-way up the pipe. Do you notice anything strange? Finally, find out if real half-pipe designs follow your suggestion.

Solution

In the given sitution we are considering that initilly the body is at rest and we are having the value of X

v=dx/dt, and accleration = d^2x/dt^2

using equation;-

V = U + at

initial velocity is 0.

we can put accelration in the above equation and can get the time.

Similarly for the other case same formula can be used but the values will be changed.