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Difficulty: MediumThe Earth as a Planet and Earth Movements

A radio station located at longitude 10∘W10^\circ\text{W} begins a live news broadcast at 2:15 p.m.2:15\text{ p.m.} local solar time. What is the local solar time at a receiving station located at longitude 35∘E35^\circ\text{E} when the broadcast is heard?

  1. A
    11:15 a.m.11:15\text{ a.m.}
  2. B
    3:55 p.m.3:55\text{ p.m.}
  3. 5:15 p.m.5:15\text{ p.m.}Answer
  4. D
    12:35 p.m.12:35\text{ p.m.}

Answer

5:15 p.m.5:15\text{ p.m.}
The correct response of 5:15 p.m.5:15\text{ p.m.} is derived by calculating the total longitudinal distance of 45∘45^\circ (10∘W+35∘E10^\circ\text{W} + 35^\circ\text{E}), converting it to a 3-hour difference (45∘/15∘=3 hours45^\circ / 15^\circ = 3\text{ hours}), and adding 3 hours to the transmitting local time (2:15 p.m.2:15\text{ p.m.}) because the destination lies to the east.

Step-by-Step Solution

1
Calculate the total angular distance between the transmitting and receiving longitudes.
10∘W+35∘E=45∘10^\circ\text{W} + 35^\circ\text{E} = 45^\circ
Since the two positions are in opposite hemispheres (West and East), their longitudinal values must be added together.
2
Convert the total angular distance into a time difference.
\frac{45^\circ}{15^\circ\text{ per hour}} = 3\text{ hours}
The Earth rotates 360∘360^\circ in 24 hours, which equals 15∘15^\circ of longitude per hour.
3
Adjust the initial local solar time according to relative direction.
2:15 p.m.+3 hours=5:15 p.m.2:15\text{ p.m.} + 3\text{ hours} = 5:15\text{ p.m.}
Because Earth rotates from west to east, locations situated further east experience solar time ahead of locations to the west.

Key Concept

Longitude and Local Solar Time Calculation
Estimated Time:1m 30s
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Topics

The Earth as a Planet and Earth Movements

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