1. **State the problem:** A ship starts at point A with coordinates $70^\circ S, 105^\circ W$ and sails due south at 50 knots for 36 hours. We need to find the coordinates of point B where the ship arrives. 2. **Calculate the distance traveled:** Speed = 50 knots means 50 nautical miles per hour. Distance traveled = speed $\times$ time = $50 \times 36 = 1800$ nautical miles. 3. **Convert distance to degrees of latitude:** 1 degree of latitude corresponds to 60 nautical miles. Degrees traveled south = $\frac{1800}{60} = 30^\circ$. 4. **Find the new latitude:** Starting latitude is $70^\circ S$. Moving 30 degrees further south means adding 30 degrees to 70 degrees south. New latitude = $70^\circ + 30^\circ = 100^\circ S$. 5. **Interpret the latitude:** Latitude cannot exceed $90^\circ$. Passing $90^\circ S$ means crossing the South Pole and continuing northward on the opposite meridian. Excess degrees beyond $90^\circ$ = $100^\circ - 90^\circ = 10^\circ$. So, the ship is $10^\circ$ north of the South Pole on the opposite meridian. 6. **Find the new longitude:** The ship started at $105^\circ W$. Crossing the South Pole reverses the longitude by 180 degrees. New longitude = $105^\circ W + 180^\circ = 285^\circ$. Since longitude is measured from $0^\circ$ to $180^\circ$ east or west, $285^\circ$ corresponds to $360^\circ - 285^\circ = 75^\circ E$. 7. **Final position of B:** Latitude $10^\circ S$ (since it is north of the South Pole, it is now in the southern hemisphere but closer to the equator), Longitude $75^\circ E$. **Answer:** The position of B is $10^\circ S, 75^\circ E$.