An aeroplane flies from a town P(lat. 40°N, 38°E) to another town Q(lat. 40°N, 22°W). It later flies to a third town T(28°N, 22°W). Calculate the : (a) dist...
Question 1 Report
An aeroplane flies from a town P(lat. 40°N, 38°E) to another town Q(lat. 40°N, 22°W). It later flies to a third town T(28°N, 22°W). Calculate the :
(a) distance between P and Q along their parallel of latitude ;
(b) distance between Q and T along their line of longitudes;
(c) average speed at which the aeroplane will fly from P to T via Q, if the journey takes 12 hours, correct to 3 significant figures. [Take the radius of the earth = 6400km ; \(\pi = 3.142\)]
Answer Details
Take \(R = 6400\) km and \(\pi = 3.142\).
(a) Distance P to Q along the parallel of latitude \(40^\circ\)N. The longitude difference is \(38^\circ\text{E} + 22^\circ\text{W} = 60^\circ\). The radius of the parallel is \(R\cos 40^\circ\), so
\[ PQ = \frac{60}{360} \times 2\pi R \cos 40^\circ = \frac{1}{6} \times 2 \times 3.142 \times 6400 \times 0.7660 = 5134\ \text{km}. \](b) Distance Q to T along the meridian \(22^\circ\)W. The latitude difference is \(40^\circ - 28^\circ = 12^\circ\), and along a meridian the radius is \(R\):
\[ QT = \frac{12}{360} \times 2\pi R = \frac{1}{30} \times 2 \times 3.142 \times 6400 = 1340.6\ \text{km}. \](c) Average speed from P to T via Q over 12 hours. Total distance:
\[ PQ + QT = 5134 + 1340.6 = 6474.6\ \text{km}. \] \[ \text{Average speed} = \frac{6474.6}{12} = 539.6 \approx 540\ \text{km/h (to 3 s.f.).} \]Download The App On Google Playstore
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