Two warships, A and B, set sail from the geographical coordinates (Lat=36.81631,Lon=30.70623) and (Lat=36.60179,Lon=36.07906) , respectively. They need to meet at the geographical location (Lat=35.38189,Lon=33.33106) ) after 4 hours. What should be the departure bearing (Azimuth Angles) and the minimum sailing speeds of warships A and B, assuming the Earth's radius is 6371 km?

To find the departure bearing and the minimum sailing speeds of warships A and B, we can use the great-circle distance formula and the spherical law of cosines.Let's denote the coordinates of warships A and B as and , respectively. The coordinates of the meeting point are .The great-circle distance formula is given by: d = R \cdot \arccos(\sin(Lat_A) \cdot \sin(Lat_M) + \cos(Lat_A) \cdot \cos(Lat_M) \cdot \cos(Lon_A - Lon_M)) where is the Earth's radius.Using the spherical law of cosines, we can find the minimum sailing speeds of warships A and B: \cos(d) = \cos(d_A) \cdot \cos(d_B) + \sin(d_A) \cdot \sin(d_B) \cdot \cos(\theta) where and are the distances traveled by warships A and B, respectively, and is the angle between their paths.Since the warships meet after 4 hours, we have and , where and are the speeds of warships A and B, respectively, and is the time taken to meet.Substituting the get: \cos(d) = \cos(v_A \cdot t) \cdot \cos(v_B \cdot t) + \sin(v_A \cdot t) \cdot \sin(v_B \cdot t) \cdot \cos(\theta) Solving this equation for and , we can find the minimum sailing speeds of the warships.The departure bearing (azimuth angle) can be found using the following formula: \tan(\theta) = \frac{\sin(Lat_M - Lat_A)}{\cos(Lat_M) \cdot \cos(Lon_M - Lon_A) - \sin(Lat_M) \cdot \sin(Lat_A)} where is the angle between the paths of the two warships.Using this formula, we can find the departure bearing for warships A and B.