. 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

d=s×t

27knots×120hrs
=3240knots
1knot=1nm
3240
3240×1= 3240nm

To calculate the distance between the two islands, we can use the formula: Distance = Speed * Time

Given:
Average speed of the ship = 27 knots
Sailing time = 120 hours

(a) Calculate the distance between the two islands:
(i) In nautical miles:

Distance = Speed * Time
Distance = 27 knots * 120 hours
Distance = 3240 nautical miles

(ii) In kilometers:

1 nautical mile = 1.852 kilometers

Distance in kilometers = Distance in nautical miles * 1.852
Distance in kilometers = 3240 nautical miles * 1.852
Distance in kilometers ≈ 6008.08 kilometers

(b) Calculate the speed of the ship in kilometers per hour:

Speed in kilometers per hour = Speed in knots * 1.852
Speed in kilometers per hour = 27 knots * 1.852
Speed in kilometers per hour ≈ 50.004 kilometers per hour

To calculate the distance between the two islands, we can use the formula:

Distance = Speed x Time

(a)

(i) To calculate the distance between the two islands in nautical miles:
Distance (in nautical miles) = Speed (in knots) x Time (in hours)
Distance = 27 knots x 120 hours
Distance = 3,240 nautical miles

(ii) To convert the distance from nautical miles to kilometers, we can use the conversion factor of 1 nautical mile = 1.852 kilometers.
Distance (in kilometers) = Distance (in nautical miles) x Conversion factor
Distance = 3,240 nautical miles x 1.852 kilometers/nautical mile
Distance = 6,002.88 kilometers (rounded to two decimal places)

Therefore, the distance between the two islands is 3,240 nautical miles or approximately 6,002.88 kilometers.

(b)

To calculate the speed of the ship in kilometers per hour, we need to convert the speed from knots to kilometers per hour. The conversion factor is 1 knot = 1.852 kilometers per hour.

Speed (in kilometers per hour) = Speed (in knots) x Conversion factor
Speed = 27 knots x 1.852 kilometers per hour
Speed = 50.004 kilometers per hour (rounded to three decimal places)

Therefore, the speed of the ship is approximately 50.004 kilometers per hour.