Code about a particle bouncing on a curved surface - c++

Question

I'm supposed to write a code that simulates an inelastic particle bouncing within a wall and a semicircle (radius 30, center # (50,0). The particle loses 3% of its original velocity every time it hits a wall and/or the semicircle.
I'm also using graphics.h library
I have made most of the program already, but the particle does not properly bounce on the semicircle.
I used the reflection matrix:
\begin{bmatrix}
cos 2\theta & sin2\theta \
sin2 \theta & -cos2\theta
\end{bmatrix}
here is the this snippet of the code containing the conditions when the particle hits the semicircle:
//initial conditions
x = 0;
y = 100;
Vx = 15.0;
Vy = 0.0;
double dt = 0.0001; //initial time step and increment
for(double t = 0; t < 50; t += dt)
{
Vy = Vy + grav*dt;
//Conditions when the particle hits a wall or the floor and retaining only 97% of its speed
if (y<0.0)
{
Vy = -Vy + grav*dt;
}
if(x >100.0 || x < 0.0)
{
Vx = -Vx;
}
//condition when the particle hits the semicircle
//semicircle equation: y = sqrt(30^2 - (x-50)^2)
if(y < sqrt((30*30)-((x-50)*(x-50))) )
{
Vxnew = ((Vx)*(cos(2.0*theta)) + (Vy*(sin(2.0*theta))));
Vy = (Vy*(cos(2.0*theta)) - ((Vx)*(sin(2.0*theta))));
Vx = Vxnew;
}
x = x + Vx*dt;
y = y + Vy*dt;
putpixel(conx(x), cony(y), 15);
}
I'm not sure if this reflection matrix applies on curved surfaces and I should use something else or my implementation is wrong.
For the losing the velocity part, I can probably just multiply the new x and y velocities by 0.97.
For context, this function that I made converts the calculated value in the loop to pixel values
//convert to pixel value (scale of 6)
double conx(double x)
{
return x * (600/100) + 50;
}
double cony(double y)
{
return -y * (600/100) + 650;
}