4) Longitude–Chronometer a. [5] At the exact moment the sun reaches it zenith ov

Question

4) Longitude–Chronometer

a. [5] At the exact moment the sun reaches it zenith over a ship at sea, the on-board chronometer indicates that the time at the Prime Meridian is 7:22 PM. Is the ship east or west of the Prime Meridian?

b. [5] However, the ship’s chronometer is known to lose 3 minutes a day and was last set 30 days prior when the ship departed its home port. What is the actual time at the Prime Meridian?

c. [5] Given that the earth turns 360° every 24 hours, how many degrees does it turn in one hour?

d. [10] What is the longitude of the ship?

e. [10] If the captain of the ship observes Polaris at 28.5° above the horizon that evening. What body of water is the ship in and what major city is it closest to?

Explanation / Answer

4) a. As given that the time of prime meridian is 7:22 pm. So, it is the evening in prime meridian. Now we know that earth rotates from east to west, so the sun must be passed over the prime meridian and stands somewhere in the west of the prime meridian. So, the ship must be in the west of prime meridian above which the sun is standing right at that time.

b. The ship's chronometer is losing 3 minutes every day. So, in 30 days it will lose 3*30=90 minutes. So, the time of the prime chronometer must be 90 minutes more than what it shows. So, the actual time of the prime chronometer is 7:22+(90 minutes)= 8:52 pm.

c. The earth rotates 360 degrees /24 = 15 degrees per hour.

d. The sun reaches its zenith over the ship. So, the time at the ship must be 12:00 am /00:00 pm. Now the difference between the time of the ship and the prime meridian is = (8:52 pm - 00:00 pm) = 8:52 hours = (8*60+52) =(480+52)= 532 minutes/ almost 9 hours. Now as we know that earth rotates 15 degrees per hours or in (60/15) four minutes it will rotate 1 degree. So, in 532 minutes it will rotate (532/4)=133 degree. So, the longitude of the ship is 133 degree west.

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