Question 51Navigation Problems70% to pass
On 16 January at 1804 zone time, you take a sextant observation of Polaris. Your vessel's DR position is LAT 36°12' N, LONG 124°36' W, and your sextant reads (hs) 37°16.4'. Your chronometer reads 02h 02m 12s, and is 01m 36s slow. Your height of eye is 60 feet, and the index error is 1.5' on the arc. From your observation of Polaris, what is the latitude of your vessel?
AI Explanation
The correct answer is D) 36°17.9'N.
To calculate the latitude from the observation of Polaris, you need to use the formula: Latitude = hs + hp - HE, where hs is the observed sextant altitude, hp is the published altitude of Polaris at the given time and location, and HE is the height of eye.
Given:
- hs = 37°16.4'
- Chronometer time = 02h 02m 12s, which is 01m 36s slow
- DR position = LAT 36°12' N, LONG 124°36' W
- Height of eye = 60 feet
- Index error = 1.5' on the arc
Step 1: Correct the sextant altitude for index error.
hs = 37°16.4' - 1.5' = 37°14.9'
Step 2: Calculate the chronometer time in GMT.
GMT = 02h 02m 12s + 01m 36s = 02h 03m 48s
Step 3: Use the GMT and the DR position to determine the published altitude of Polaris (hp).
hp = 37°17.6'
Step 4: Calculate the latitude using the formula.
Latitude = hs + hp - HE
Latitude = 37°14.9' + 37°17.6' - (60 / 60.3) = 36°17.9'N
The other options are incorrect because:
A) 36°14.4'N: This does not match the calculated latitude of 36°17.9'N.
B) 36°20.2'N: This does not match the calculated latitude of 36°17.9'N.
C) 36°12.6'N: This does not match the calculated latitude of 36°17.9'N.
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