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A) What is the time difference between B and C? b) A plane flying due south from A to B at 900 knots takes 7 hours. Find the difference in latitude between A and B.

Geography

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Answers

2 parts
a

7 hours\text{7 hours}

b

105∘\text{105}^\circ

Step-by-step solution

5 steps

Part a· 3 steps

What is the time difference between B and C?

  1. Determine the longitudes of points B and C.

    From the diagram, point B is at 40∘40^\circ W longitude.
    From the diagram, point C is at 65∘65^\circ E longitude.

  2. Calculate the difference in longitude.

    Since B is in the West and C is in the East, the total difference in longitude is the sum of their longitudes.

    Difference in longitude=40∘+65∘=105∘\text{Difference in longitude} = 40^\circ + 65^\circ = 105^\circ

  3. Convert the longitude difference to time difference.

    The Earth rotates 360∘360^\circ in 24 hours. This means 1∘1^\circ of longitude corresponds to 24 hours360∘=115\frac{24 \text{ hours}}{360^\circ} = \frac{1}{15} hours, or 60 minutes15=4\frac{60 \text{ minutes}}{15} = 4 minutes.

    Time difference=105∘×4 minutes1∘=420 minutes\text{Time difference} = 105^\circ \times \frac{4 \text{ minutes}}{1^\circ} = 420 \text{ minutes}

    To convert minutes to hours:

    Time difference=420 minutes60 minutes/hour=7 hours\text{Time difference} = \frac{420 \text{ minutes}}{60 \text{ minutes/hour}} = 7 \text{ hours}

    The time difference between B and C is 7 hours\boxed{\text{7 hours}}.

Part b

105∘\text{105}^\circ

A plane flying due south from A to B at 900 knots takes 7 hours. Find the difference in latitude between A and B.

  1. Calculate the distance traveled by the plane.

    The speed of the plane is 900 knots. A knot is 1 nautical mile per hour (nm/h).
    The time taken is 7 hours.

    Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time} Distance=900 nm/h×7 h=6300 nautical miles\text{Distance} = 900 \text{ nm/h} \times 7 \text{ h} = 6300 \text{ nautical miles}

  2. Convert the distance in nautical miles to a difference in latitude.

    One nautical mile is defined as the length of one minute of arc along a great circle (like a meridian).
    There are 60 minutes in 1∘1^\circ. Therefore, 1∘1^\circ of latitude corresponds to 60 nautical miles.

    Difference in latitude=Distance in nautical miles60 nautical miles/degree\text{Difference in latitude} = \frac{\text{Distance in nautical miles}}{60 \text{ nautical miles/degree}} Difference in latitude=6300 nm60 nm/degree=105∘\text{Difference in latitude} = \frac{6300 \text{ nm}}{60 \text{ nm/degree}} = 105^\circ

    The difference in latitude between A and B is 105∘\boxed{\text{105}^\circ}.

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