A ship leaves an island (5°N, 45° E) and sails due east for 120 hours to another island. Average speed of the ship is 27 knots.
(a) Calculate the distance between the two islands
(i) In nautical miles
(ii) In kilometers
(b) Calculate the speed of the ship in kilometers per hour
To calculate the distance between the two islands, we first need to determine the latitude and longitude of both islands.
The starting island is located at 5°N, 45°E. Since the ship sails due east, we can assume that the latitude remains the same, making the position of the second island 5°N, 45°E + 120 hours east.
(a) Calculate the distance between the two islands:
(i) In nautical miles:
To calculate the distance in nautical miles, we can use the formula:
Distance = Speed x Time
Given that the average speed of the ship is 27 knots and it sails for 120 hours, the distance can be calculated as follows:
Distance = 27 knots x 120 hours = 3240 nautical miles
(ii) In kilometers:
To convert the distance from nautical miles to kilometers, we use the conversion factor that 1 nautical mile is equal to 1.852 kilometers.
So, the distance in kilometers can be calculated as follows:
Distance (km) = Distance (nautical miles) x 1.852
Distance (km) = 3240 nm x 1.852 = 5998.08 kilometers
(b) Calculate the speed of the ship in kilometers per hour:
To convert the speed from knots to kilometers per hour, we use the conversion factor that 1 knot is equal to 1.852 kilometers per hour.
So, the speed of the ship in kilometers per hour can be calculated as follows:
Speed (km/h) = Speed (knots) x 1.852
Speed (km/h) = 27 knots x 1.852 = 49.404 kilometers per hour