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A jet flies from town X (50°S, 20°E) directly to Y(50°S, 28°W) and 1200m to Z (i) Find the latitude of Z (ii) Calculate the distance XY along a parallel of latitude 50°S in km (i) Given that the average speed of the jet is 400 knots, calculate the time taken to

Mathematics

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Kuhusu swali namba 12:

Tunapewa pointi A na B kwenye duara moja la latitudo na umbali mfupi zaidi kati yao ni 2133.6 km. Tunatakiwa kupata mahali pa B.

Hatua za Kutatua:

Tunatumia formula ya umbali mfupi zaidi kwenye duara kuu:

d=Rθd = R \theta

Ambapo:

  • d=2133.6 kmd = 2133.6 \text{ km}
  • R=6380 kmR = 6380 \text{ km}
  • θ\theta ni tofauti ya angular kati ya A na B.
  1. Pata θ\theta

    2133.6=6380θ2133.6 = 6380 \theta θ=2133.66380\theta = \frac{2133.6}{6380} θ≈0.3345 radiani\theta \approx 0.3345 \text{ radiani}
  2. Badilisha θ\theta kuwa digrii

    θ=0.3345×180π\theta = 0.3345 \times \frac{180}{\pi}

    Tumia π=227\pi = \frac{22}{7}:

    θ≈0.3345×180×722\theta \approx 0.3345 \times \frac{180 \times 7}{22} θ≈19.17∘\theta \approx 19.17^\circ
  3. Pata longitudo ya B

    Kwa kuwa A iko kwenye (70∘N,15∘E)(70^\circ \text{N}, 15^\circ \text{E}), na B iko kwenye latitudo sawa, tofauti ya longitudo ni 19.17∘19.17^\circ.

    Kwa hivyo, longitudo ya B ni 15∘E+19.17∘=34.17∘E15^\circ \text{E} + 19.17^\circ = 34.17^\circ \text{E}.

    Mahali pa B:

    B(70∘N,34∘E)B(70^\circ \text{N}, 34^\circ \text{E})

    Jibu:

    B(70∘N,34∘E)\boxed{B(70^\circ \text{N}, 34^\circ \text{E})}

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