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Solving projectile launch

A ball is fired from the center of Ban Jelačić Square in Zagreb (45°48'47.4"N 15°58'38.3"E) at an angle of 45 degrees, in eastward direction. The ball is fired at 12:00:00 GMT on January 1, 2024. What is position of the ball after one hour, for following values of the initial velocity:

  1. 10 m/s
  2. 100 m/s
  3. 500 m/s
  4. 1000 m/s
  5. 5000 m/s
  6. 10000 m/s
  7. 2e4 m/s (20 km/s)
  8. 1e5 m/s (100 km/s)
  9. 1e6 m/s (1000 km/s)
  10. 3e7 m/s? (0.1c)
  11. 1e8 m/s (0.333c)
  12. 2.5e8 m/s (0.833c)

Air resistance is ignored. For the first 6 cases, specify solution in (latitude, longitude, height) coord. system. For the last 6 cases ... specify planetary coordinate system?.

C++ file with implementation