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.
<h3>(a) Distance A-B</h3>
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.
<h3>(b) Time A-B</h3>
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.
<h3>(c) Latitude of point C</h3>
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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<em>Additional comment</em>
Using a different approximation for pi will change the AB distance by a few km.
