// ...
#define _USE_MATH_DEFINES
#include <math.h>

class MainView : public CWnd {
// ...
private:
// ...
#define XNAUGHT 0.0 // starting x-position (in meters)
#define YNAUGHT 0.0 // starting y-position (in meters)
#define VNAUGHT 0.5 // starting vector velocity magnitude (in meters/second)
#define THETA (M_PI / 4) // starting vector velocity angle (in radians)
#define GRAVITY 9.81 // value of g (in meters/second^2)
#define TIME_INCREMENT 0.001 // amount to add to t in each frame
  double vx; // x-component of vector velocity (in meters/second)
  double vy; // y-component of vector velocity (in meters/second)
  double x; // x-position (in meters)
  double y; // y-position (in meters)
  double t; // time (in seconds)
  double tland; // time of landing (in seconds)
// ...
  friend class Animator; // definition below
  Animator *animator;
// ...
};

// note: this class works as a thread class, it's just here for clarity
class Animator : public CWinThread {
  DECLARE_DYNCREATE(Animator)
public:
  virtual BOOL InitInstance() { m_bAutoDelete = TRUE; return TRUE; }
  virtual int ExitInstance() { return CWinThread::ExitInstance(); }
protected:
  afx_msg void onBegin(WPARAM wParam, LPARAM lParam);
  afx_msg void onEnd(WPARAM wParam, LPARAM lParam) { ::PostQuitMessage(0); }
  DECLARE_MESSAGE_MAP()
};

// ...

MainView::MainView() {
  vx = VNAUGHT * cos(THETA);
  vy = VNAUGHT * sin(THETA);
  x = XNAUGHT;
  y = YNAUGHT;
  t = 0.0;
// ...
  double range = ((VNAUGHT * VNAUGHT) / GRAVITY) * sin(2.0 * THETA);
  tland = range / (VNAUGHT * cos(THETA);
}

// ...

IMPLEMENT_DYNCREATE(Animator, CWinThread)

BEGIN_MESSAGE_MAP(Animator, CWinThread)
  ON_THREAD_MESSAGE(WM_USER, onBegin)
  ON_THREAD_MESSAGE(WM_USER + 1, onEnd)
END_MESSAGE_MAP()

void Animator::onBegin(WPARAM wParam, LPARAM lParam) {
  MainView *mv = (MainView *)lParam;
  Sleep(1000);
  do {
    Sleep(100);
    mv->t += TIME_INCREMENT;
    mv->y += mv->vy * mv->t - 0.5 * GRAVITY * mv->t * mv->t;
    mv->vy = VNAUGHT * sin(THETA) - GRAVITY * mv->t;
    mv->x += mv->vx * mv->t;
// ...
// convert meters to pixels and post paint message
// ...
  } while(mv->t < mv->tland / 2.0);
// ...
// the loop is split into two b/c I have two different images for ascending and
// descending (code for handling not shown)
// ...
  do {
    Sleep(100);
    mv->t += TIME_INCREMENT;
    mv->y += mv->vy * mv->t - 0.5 * GRAVITY * mv->t * mv->t;
    mv->vy = VNAUGHT * sin(THETA) - GRAVITY * mv->t;
    mv->x += mv->vx * mv->t;
// ...
  } while(mv->t < mv->tland);
// ...
}