A scientific research vessel positioned at longitude 48.5^\circ\text{W} records its local … — JAMB UTME

A scientific research vessel positioned at longitude $48.5^\circ\text{W}$ records its local solar time as 3:34 p.m. At that exact instant, a terrestrial tracking station records its local solar time as 9:10 a.m. on the same day. What is the longitude of the tracking station in degrees West?

Answer: 144.5 °W

Answer

The longitude of the tracking station is

144.5^\circ\text{W}

The difference in local solar time between 3:34 p.m. (15:34) and 9:10 a.m. (09:10) is 6 hours and 24 minutes, or 384 minutes. Dividing 384 minutes by 4 minutes per degree gives a longitude difference of

96^\circ

. Since the tracking station is behind in time relative to the vessel, it must be located west of

48.5^\circ\text{W}

. Adding

96^\circ

westward yields a final longitude of

144.5^\circ\text{W}

Step-by-Step Solution

Calculate the total time difference between the vessel and the tracking station.

Time difference = 15:34 - 09:10 = 6 hours and 24 minutes = 384 minutes.

Determining the net difference in local time is required to find the angular displacement.

Convert time difference in minutes to degrees of longitude.

Longitudinal distance = 384 minutes / 4 minutes per degree = 96 degrees.

Earth rotates

360^\circ

in 24 hours, which corresponds to

1^\circ

of longitude every 4 minutes.

Apply the longitudinal directional rule ('West lose, East gain') to find the station's location.

Station longitude = 48.5 degrees W + 96 degrees = 144.5 degrees W.

Since the tracking station's local time is behind the vessel's local time, the station must be positioned further west of the vessel.

Key Concept

Longitude calculation from local solar time differences and Earth's axial rotation rate

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