L = 1.524;
g =9.81;
h2=.12;
e =.74;
TableForm[{{Slider[Dynamic[θ],{0,N[Pi]/2}],Dynamic[θ],"θ"},
{Slider[Dynamic[xi],{0,3}],Dynamic[xi],"(Subscript[x, i])"},
{Slider[Dynamic[H], {0,10}],Dynamic[H], "H"}}]

Dynamic[Yexit = H-Sin[θ]*L] "=Yexit"
Dynamic[Xexit = -xi + Cos[θ] L] "=Xexit"
Dynamic[Vye=-Sin[θ]* Sqrt[2*g*Sin[θ]*L]] "=Vye"
Dynamic[Vxe=Cos[θ]* Sqrt[2*g*Sin[θ] *L ]] "=Vxe"
Dynamic[t1 =t/.Solve[0== Yexit+Vye * t +-1/2 g t^2,t][[2]]] "=t1"
Dynamic[Vyf= -e(Vye-g*t1)]  "=Vyf"
Dynamic[t2= t /. Solve[h2 == 0 + Vyf *t - 1/2 g t^2,t][[2]]]"=t2"
Dynamic[x1 = (Cos[θ]*L - xi) + Vxe * t1] "=x1"
Dynamic[x2= x1+ Vxe*t2] "=x2"

Dynamic[y = Piecewise[{{Yexit+Vye*t+-1/2g t^2, t < t1},{0+Vyf*(t-t1)+-1/2g (t-t1)^2,t ≥ t1}}]]

Dynamic[Manipulate[Show[
Graphics[{Blue, Circle[{(Xexit+Vxe*j)/.{θ->1},y/.{t->j}},.0345],Rectangle[{.743,0},{.743+.063,.33}],Black,Rotate[Rectangle[{-xi,H},{-xi+L,H+.05}],-θ,{-xi,H}]
, Red, Rectangle[{1.5,0},{1.5+.28,.12}]
},Axes -> True, AxesOrigin->Automatic , PlotRange->{{-1,2},{-1,2}}]
,ParametricPlot[{Xexit+Vxe*x,y/.{t->x}},{x,0,t1+t2}]],{j,0,t1+t2}]]/.{θ->1}

The following section requires modification to the above code to work. To produce a parametric plot one of the slider for the control varaiables must be disabled and the variable value cleared.

ParametricPlot[{(Xexit+Vxe*x)/.{xi-> j},y/.{t->x,xi-> j}},{x,0,(t1+t2)/.{xi-> 1.5}}, {j,1.2,2},PlotRange->{{-1,2},{-1,2}},Mesh->{200,23}, PerformanceGoal:>"Quality",WorkingPrecision->MachinePrecision]