(a) Two points X(32^\circN, 47^\circW) and Y(32^\circN, 25^\circE) are on the earth's surface. If it takes an aeroplane 11 hours to fly from X to Y along the parallel of latitude, calculate its speed, correct to the nearest kilometre per hour. [Radius of the earth = 6400km; \(\pi = \frac{22}{7}\)]
(b) Two observers P and Q, 15metres apart observe a kite (K) in the same vertical plane and from the same side of the kite. The angles of elevation of the kite from P and Q are 35^\circ and 45^\circ respectively. Find the height of the kite to the nearest metre.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Difference in longitude = 47^\circ + 25^\circ = 72^\circ
Distance /XY/ = \(\frac{\theta}{360^\circ} \times 2\pi r\)
Where \(r = R \cos 32^\circ\)
\(\therefore /XY/ = \frac{72}{360} \times 2 \times \frac{22}{7} \times 6400 \times \cos 32\)
= \(2 \times \frac{22}{7} \times 1280 \times 0.8480\)
= \(6822.765km\)
\(Speed = \frac{Distance}{Time}\)
= \(\frac{6822.766}{11} = 620.25 km/h\)
(b) \
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Source: Myschool Past Questions Archive (Record #54560)