3. A plane leaves an airport X, 20....
Question

# 3. A plane leaves an airport X, 20.6°E and 36.8°N, and flies due South along the same longitude for 8 hours at the rate of 1,000km/h, to another airport Y, 20.6°E and 6°S. The plane then flies West to another airport Z for 8 hours at the same speed. Calculate, to the nearest degree, a) the value of 0, and b) the longitude of Z. (Take radius R of the earth = 6,400km).

JEE/Engineering Exams
Maths
Solution
72
2.7 (3 ratings)
The radius of earth is ( 6371 mathrm{km} ) We have ( mathrm{r} theta=8000, ) so ( theta=8000 / 6371=71.9^{circ} ) Y is at ( 20.6^{circ} mathrm{E} 35.1^{circ} mathrm{S} ) Now, at latitude ( emptyset ), the radius of the circle of latitude is ( r^{prime}=r cos emptyset ) So, ( r^{prime}=6371 cos 35.1^{circ}=5210 mathrm{km} ) At that latitude, ( 8000 mathrm{km} ) is ( 88.0^{circ} ) ( mathrm{Z} ) is at ( 67.4^{circ} mathrm{W} 35.1^{circ} mathrm{S} ) ( mathrm{Z} ) is thus at