$\mathrm{surf}≔ \sin \left(x\right)+\left(0.2\cos \left(4x+ \sin \left(4x\right)\right)\right)-0.2 x\+3\:$

$\mathrm{plot}\left(\mathrm{surf}\,x=0..10\,\mathrm{scaling}=\mathrm{constrained}\right)$

$V≔\mathrm{Vector}\left(\left[\stackrel{\mathbf{.}}{x}\left(t\right)\,\stackrel{\mathbf{.}}{y}\left(t\right)\right]\right)\:$

$N≔\mathrm{LinearAlgebra}:-\mathrm{Normalize}\left(\mathrm{Vector}\left(\left[\left[-\left(\frac{\partial }{\partial x}\mathrm{surf}\right)\right]\,\left[1\right]\right]\right)\,2\,\mathrm{conjugate}=\mathrm{false}\right)\mathbf{assuming} \mathrm{positive}\:$

$N≔\mathrm{eval}\left(N\,x=x\left(t\right)\right)$

$N:=\left[\begin{array}{c}\frac{-\cos \left(x\left(t\right)\right)\+0.2\sin \left(4x\left(t\right)\+\sin \left(4x\left(t\right)\right)\right)\left(4\+4\cos \left(4x\left(t\right)\right)\right)\+0.2}{\sqrt{1\+{\left(-\cos \left(x\left(t\right)\right)\+0.2\sin \left(4x\left(t\right)\+\sin \left(4x\left(t\right)\right)\right)\left(4\+4\cos \left(4x\left(t\right)\right)\right)\+0.2\right)}^2}}\\ \frac{1}{\sqrt{1\+{\left(-\cos \left(x\left(t\right)\right)\+0.2\sin \left(4x\left(t\right)\+\sin \left(4x\left(t\right)\right)\right)\left(4\+4\cos \left(4x\left(t\right)\right)\right)\+0.2\right)}^2}}\end{array}\right]$

$\mathrm{V\_reflect}≔-\left(1\+\mathrm{C\_\_R}\right) \left(\mathrm{V}\.\mathrm{N}\right)\mathrm{N}\+\mathrm{V}\:$

$\mathrm{V\_reflect}\mathit{:=}\mathrm{simplify}\left(\mathrm{V\_reflect}\,\mathrm{symbolic}\right)\:$

$\mathrm{C\_\_R} ≔ 0.99\:$

$\mathrm{deqs}≔\stackrel{\mathbf{..}}{y}\left(t\right)=-9.81,\stackrel{\mathbf{..}}{x}\left(t\right)=0\:$

$\mathrm{ics}≔\mathrm{D}\left(x\right)\left(0\right)=0,\mathrm{D}\left(y\right)\left(0\right)=0,x\left(0\right)=2,y\left(0\right)=4.5\:$

$$\begin{gathered} \mathrm{sol}≔\mathrm{dsolve}\left(\left\{\mathrm{deqs}\,\mathrm{ics}\right\}\,\left\{x\left(t\right)\,y\left(t\right)\right\}\,\mathrm{numeric}\, \\ \mathit{events}\=\left[\left[y\left(t\right)=\mathrm{eval}\left(\mathrm{surf}\,x=x\left(t\right)\right)\,\left[\mathrm{temp}=\stackrel{\mathbf{.}}{x}\left(t\right)\,\stackrel{\mathbf{.}}{x}\left(t\right)= {\mathrm{V\_reflect}}_1\,\stackrel{\mathbf{.}}{y}\left(t\right)= \mathrm{subs}\left(\stackrel{\mathbf{.}}{x}\left(t\right)=\mathrm{temp}\,{\mathrm{V\_reflect}}_2\right)\right]\right]\right]\, \\ \mathrm{range}\=0..10\, \\ \mathrm{output}\=\mathrm{listprocedure}\right)\: \end{gathered}$$

$\mathrm{xanim}≔\mathrm{subs}\left(\mathrm{sol}\,x\left(t\right)\right)\:$$\mathrm{yanim}≔\mathrm{subs}\left(\mathrm{sol}\,y\left(t\right)\right)\:$

$\mathrm{p1}≔\mathrm{plot}\left(\mathrm{surf}\,x=0..10\,\mathrm{color}=\mathrm{black}\,\mathrm{filled}\=\mathrm{true}\, \mathrm{transparency}\=0.5\right)\:$$\mathrm{p2}≔\mathrm{animate}\left(\mathrm{pointplot}\,\left[\left[\mathrm{xanim}\left(t\right)\,\mathrm{yanim}\left(t\right)\right]\,\mathrm{symbol}=\mathrm{solidcircle}\,\mathrm{symbolsize}=15\,\mathrm{color}=\mathrm{black}\right]\,t=0..10\,\mathrm{frames}=150\right)\:$

$\mathrm{display}\left(\mathrm{p1}\,\mathrm{p2}\,\mathrm{view}=\left[0..10\,0..5\right]\,\mathrm{scaling}=\mathrm{constrained}\right)$