Question

A plane flies due East from A(lat.53°N, long. 25°E) to a point B(lat. 53.°N, Ilong. 85°E) at an average speed of 400 km/h. The plane then flies South from B to a point C 2000km away. Calculate, correct to the nearest whole number: (a) the distance between A and B; (b) the time the plane takes to reach point B; (c) the latitude of C. [Take the radius of the earth to be 6400 km and : = 22/7)​

Answer 1

Answer:

  (a) 4035 km

  (b) 10 h

  (c) 35°

Step-by-step explanation:

For the purpose here, we assume the Earth is a sphere, the radius to the path of the airplane is 6400 km, and pi = 22/7. We further assume that each path is part of a circle of appropriate radius.

(a) Distance A-B

The distance from A to B will be the length of the latitude line between 25°E and 85°E, a change in longitude of 60°. The radius of the circular path along latitude line 53° is ...

  (6400 km)×cos(53°) ≈ 3851.616 km

The length of the path from A to B is given by ...

  s = rθ . . . . where θ is in radians

  s = (3851.616 km)(π/3) = (3851.616 km)(22/(7·3)) ≈ 4035 km

The distance from A to B is about 4035 km.

(b) Time A-B

The time is the ratio of distance to speed:

  t = d/r = (4035 km)/(400 km/h) = 10 h

The time taken to reach point B is 10 hours.

(c) Latitude of point C

Using the above relation for arc length, we can find the angle associated with an arc length of 2000 km.

  θ = s/r = (2000 km)/(6400 km) = 5/16 . . . . radians

The conversion to angle is ...

  degrees = radians × 180/π

  degrees = (5/16)(180/(22/7)) = 5·180·7/(16·22) = 17 79/88 ≈ 18

Point C is 18° closer to the equator than latitude 53°, at latitude 35°.

The latitude of C is 35°.

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Additional comment

Using a different approximation for pi will change the AB distance by a few km.