a) What is the time difference between B and C? b) A plane flying due south from A to B at 900 knots takes 7 hours. Find the difference in latitude between A and B.

a) What is the time difference between B and C? Step 1: Determine the longitudes of points B and C. From the diagram, point B is at 40^ W longitude. From the diagram, point C is at 65^ E longitude. Step 2: Calculate the difference in longitude. Since B is in the West and C is in the East, the total difference in longitude is the sum of their longitudes. Difference in longitude = 40^ + 65^ = 105^ Step 3: Convert the longitude difference to time difference. The Earth rotates 360^ in 24 hours. This means 1^ of longitude corresponds to 24 hours360^ = (1)/(15) hours, or 60 minutes15 = 4 minutes. Time difference = 105^ × 4 minutes1^ = 420 minutes To convert minutes to hours: Time difference = 420 minutes60 minutes/hour = 7 hours The time difference between B and C is 7 hours. b) A plane flying due south from A to B at 900 knots takes 7 hours. Find the difference in latitude between A and B. Step 1: Calculate the distance traveled by the plane. The speed of the plane is 900 knots. A knot is 1 nautical mile per hour (nm/h). The time taken is 7 hours. Distance = Speed × Time Distance = 900 nm/h × 7 h = 6300 nautical miles Step 2: Convert the distance in nautical miles to a difference in latitude. One nautical mile is defined as the length of one minute of arc along a great circle (like a meridian). There are 60 minutes in 1^. Therefore, 1^ of latitude corresponds to 60 nautical miles. Difference in latitude = Distance in nautical miles60 nautical miles/degree Difference in latitude = 6300 nm60 nm/degree = 105^ The difference in latitude between A and B is 105^. That's 2 down. 3 left today — send the next one.