Answer Key - Assignment 3 Time and Direction

For this Assignment, assume that it is not Daylight Savings Time. Refer to the appropriate Tutorial (Navigation at Sea and Time)  to complete this homework. Answer the questions directly in Canvas. For assistance, review Unit 0.21 "Turning in Assignments".

Please use this online time zone map (Links to an external site.) to complete your homework. If you are able, you may find it easier to print out a copy of this map.

  1. How many time zones are in the 50 United States? There are six (6) time zones in the US ( do not forget Hawaii and Alaska - the are part of the 50 states)

 

  1. If it is 3 p.m. in New York City, then it is what time in Honolulu?

10 a.m.

 

  1. If it is 3 a.m. Tuesday in Tokyo, then in San Francisco it is what time and day?

Monday, 10 a.m. (You crossed the dateline so the day changed)

  1. If it is 7 p.m. Friday in Rome, then in Hong Kong it is what time and day?

Saturday, 2 a.m. (You crossed the dateline and you went through midnight)

  1. Suppose you are drifting in a lifeboat in the ocean. You observe the Sun is directly overhead as you hear on the radio that it is 5 p.m. in Los Angeles. You happen to know that LA is located at 120° west longitude. Your longitude in the lifeboat is what? (remember to include east or west)

If the sun is directly overhead at your lifeboat, know that it is noon on your lifeboat.

It is 5 pm in LA. Therefore, the time on your lifeboat is 5 hours behind LA time

Each hour of time equals 15° of longitude (see tutorial and Canvas notes) so 5 hours difference is 5 x 15 or 75° separate your lifeboat from LA.

Since it is earlier on your lifeboat, we can assume that you are west of LA (remember time is always earlier to the west) so you are 75° longitude west of LA

You aren't finished yet, because you have to figure out what meridian of longitude lies 75° west of LA.

As you go west of LA, out in the Pacific you hit a very important meridian - the International dateline 180°. So degrees of Longitude increase until you hit the dateline then they start to decrease until you hit 0° at the Prime Meridian. Once you cross the 180th meridian you are also in the Eastern Hemisphere.

So your life boat is located at 165°E

Draw yourself a picture. It will help

  1. Later in the day, still in the lifeboat you observe the star Polaris 19° above the horizon. What is your latitude?

Latitude is much simpler

If you are seeing Polaris (the North Star) you are in the Northern Hemisphere.

The angle of Polaris above the horizon equals your latitude. That's it...no math, nothing complicated

Lifeboat Latitude is 19°N

 

  1. On a different voyage you ship goes down again! And you are again drifting in a lifeboat. Your watch is set to New York time and reads 3 p.m. but you observe that the sun is just setting. Soon after, you see Polaris very close to the horizon. What is your longitude (you will need to find the longitude of NYC to answer this)?

So you know that it is 3 pm in NYC and that it is sunset where your lifeboat is. But I didn't tell you the longitude for NYC or give you a direct time for your lifeboat.

Finding the longitude of NYC is easy - look it up online. It's 74°W

But what time is sunset? The next sentence is the clue "you observer Polaris very close to the horizon".  If the angle of Polaris above the horizon equals your latitude then Polaris is very close to zero (because the angle above the horizon is close to zero). So this means your boat is near the Equator.

What has this got to do with the time at sunset? As you read in Canvas and learned in lecture, the length of day is always 12 hours at the Equator. The sun always rises and sets at about 6. So sunset on your lifeboat is 6 pm.

Now you have all the pieces.  6 pm on the boat and 3 pm in NYC, 3 hours x 15° = 45° of longitude..

So your lifeboat is 45° from NYC. Is it east or west? Since its later on the boat, the boat is East of NYC so  you are 45° east of NYC.

Finally, you need to figure out what meridian is 45° longitude east of NYC (which is 74°W). So east of NYC, if you go far enough, is the Prime Meridian (0°) in England. So the meridians are decreasing as you cross the Atlantic

74° - 45° = 29°W is your longitude on the boat. Since you haven't travelled beyond the Prime Meridian you remain in the western hemisphere.

Look at a world map or a globe, if you have one. It will help.

 

  1. What is your latitude?

Because Polaris is very close to the horizon, the angle is very close to zero so your latitude is very close to 0°

 

  1. Find a World Map online with meridians and parallels (if you happen to have access to a globe, you may find it a better tool than a map to use for this problem).  Estimate how far it is from Quito, Ecuador to Singapore. The trick is to know about latitude, longitude their relationship to distance, and the circumference of the the Earth. Once you figure out the trick, the calculation is a snap.

Quito (0°S, 78°W) and Singapore (1°N, 103°E)  are both located almost directly on the Equator. They are also almost exactly 180° longitude apart. So to estimate quickly how far apart they are you can either multiply 69 x 181 = 12,489 miles (why 69? because at the equator there are 69 miles between degrees of longitude) or since they are 180 degrees apart they are half the circumference of the Earth which is 24,901 miles. Half the circumference is 12,450 miles.

I accepted any answer within 5% of 12,489 since you were asked to estimate ( 11, 864 to 13,113)