Question

Please anyone to show me how this mathematics question is done..please

Answer 1

9514 1404 393

Answer:

  (i) 55.59 km/h

  (ii) 3600 nautical miles ≈ 6670.8 km

  (iii) 30°N 29.3°E

Step-by-step explanation:

(i) The speed in km/h requires a units conversion.

  (30 kt/h)(1.853 km/kt) = 55.59 km/h

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(ii) Here, we assume we're interested in the distance traveled. If the course is "due east", we presume that means it follows the 30° latitude line, so is not the shortest route between A and B. That is, the distance from A to B will be different from the distance traveled. (The shortest route from A to B is along a great circle.)

  distance = speed × time

  distance = (30 kt/h)(120 h) = 3600 nautical miles

  = (55.59 km/h)(120 h) = 6670.8 km

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(iii) The radius of the 30° latitude line is ...

  (6370 km)(cos(30°)) = 3185√3 km ≈ 5516.58 km

The relationship between arc length (s) and central angle (α) is ...

  s = rα

So, the change in the vessel's longitude is ...

  α = (6670.8 km)/(5516.58 km) ≈ 1.20923 radians ≈ 69.28°

Then town B has longitude ...

  40°W -69.3° = -29.3°W = 29.3°E

The position of town B is about 30°N 29.3°E.

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Additional comment

The route supposedly taken by this sea vessel is from the middle of the North Atlantic to a town in northern Egypt, through the northern Sahara desert. The eastern end point is shown in the attachment.

Some spherical trigonometry is involved if you want to find the end point of the great-circle route of the same length.