@max125 it is an excercise in google translate.  Luckily not too much work for me to do for you.  I have uploaded the worksheets translated in english.

Curvilinear_Acceleration.mw
Use_of_commands_and_operators_for_calculations_of_acceleration_components.mw

@Carl Love what is harder is given an answer of sqrt(6)/6, how is it manipulated to 1/sqrt(6) ?

Fair enough.  That will do.

I can't see why you would have to convert the radical to a floating point for it to work. 

Is there a situation where sqrt of a some random number would cause sign to fail?

Curiously how did you convert 1/6* √6 to just 1/ √6

Using remove to remove the sets containing k[d2]=k[d1] is from Sa1 is

remove(s->true in map(has,s,k[d2]=k[d1]),Sa1)  # remove sets containing k[d2]=k[d1]

Strangely remove(s->false in map(has,s,k[d2]=k[d1]),Sa1) doesn't produce the other two sets as I think it should. 

map(has,Sa1,k[d2]=k[d1])
                 

If I read the command that I just wrote down, I would take that as remove the set NOT containing k[d2]=k[d1]
                            

@tomleslie Equation number and labels are 1 to 1 until you use a plot in your worksheet. 

So the workaround is to use the Retrieve command generated by the context menus in worksheet mode.

Should I submit a problem report?

@acer Ok Retrieve works unless it seems, if there is a plot in the document, Retrieve runs into issues. 

I'm using Windows 7 64 bit Maple 2018 document mode.  I've uploaded my test file.test1.mw

Using Insert->Reference, as suggested by Tomleslie will insert label (1) - the only option from the file but it is shown like this

otherwise using the Retrieve command fails

**edit added**
actually using worksheet mode I can see L1 actually turns out to be L36 !

But my point is plot is causing the mixups.

I downloaded an mw file off of mapleprimes.  Saved it in the file location as one can see in the original post.

FileTools:-IsReadable("c:/test/testing.mw")
                                                                   True

DocumentTools:-Retrieve("c:/test/testing.mw","L1")

The error pops up again.

 

@Preben Alsholm ok yes so what we need to do is add code that says when it's at a certain level it follows a ball constrained to a curve, until it hits some point where it gets launched into the air at which point it will have to follow the original code again.  I don't know how easy it can be done.

@Preben Alsholm if you change your # of hits to 1000 the ball still stops in the exact location as 100hits and you get the error

Warning, cannot evaluate the solution further right of 5.1979218, maxfun limit exceeded (see ?dsolve,maxfun for details)

@Jaqr I believe some time ago there was an issue using ? in a web address name.  I think the solution for that was to double up on the question marks?  I think that issue was resolved, but give it a try.

**edit added**  Actually the double ?? was for older versions of Maple using HTTP[Get] so I don't think it applies in your situation. Wouldn't hurt to give it a try though.

I think the final satisfactory solution lies in the events part of the code

Can't think straight, I was trying to apply Acer's piecewise approach by changing the events to something like

events := [[y(t) = eval(surf, x = x(t)), [diff(y(t), t) = piecewise(abs(diff(y(t), t)) < 0.1e-1, abs(diff(y(t), t)), [temp = diff(x(t), t), diff(x(t), t) = V_reflect[1], diff(y(t), t) = subs(diff(x(t), t) = temp, V_reflect[2])])]]]

In Roubens solution, when the bounces get too small the code stops, that is maxfun limit is exceeded.  How do we hold the ball at small bounces so we can continue the code until motion in the y direction becomes small as well?

@Rouben Rostamian  Nice work Rouben!

edit added** however it seems the solution still can't proceed beyond certain points. 

Setting these parameters (just for example) CR:=.55,  and initial conditions x(0):=2 y(0):=4.5 and the other ic conditions set to 0.  The animation ends as the ball rolls down the hill. 

I expect it has something to do with infintesimally small bounces?  Eventually hope the animation can end with the ball ending up in one of the troughs.