3) Longitude–DeadReckoning a. [5] Given that the earth has a circumference of 40

Question

3) Longitude–DeadReckoning

a. [5] Given that the earth has a circumference of 40,075 km at the equator, how long is one degree of longitude in kilometers at the equator?

b. [5] The following is the equation to calculate the length of one degree of longitude (L) at a given latitude (lat) based on the length of one degree of longitude at the equator (Leq) : L = Leq * cos(lat)

Find the length of one degree of longitude in kilometers at a latitude of 28°

c. [5] On a 50 meter long ship sailing due west from the Canary Islands (latitude = 28° N) a piece of wood is dropped in the water at the bow (front of the ship) and timed as it floats down the side of the ship until it reaches the stern (back of the ship). Over the course of many such observations, it takes at a minimum of 18 seconds for the ship to pass the piece of wood and a maximum of 20 seconds. What is the minimum and maximum speed of the ship in kilometers per hour?

d. [10] If the ship started in the Canary Islands at the coordinates 28° 00’ 00” N and 18° 00’ 00” W and sailed due west, what is the minimum and maximum distance in kilometers it could have traveled in 120 hours?

e. [5] What is the new longitude for the ship (give minimum and maximum possible longitude)

f. [5] What is the distance between the minimum and maximum possible longitude in kilometers?

g. [5] Name and describe at least three possible sources of error in calculating a position this way.

Explanation / Answer

Answer : Only 4 question answered as per chegg's rule

(a) At equator, 1° longitutde = (40075/360) = 111.319 km.

(b) By the given,   

L=Leq * cos (lat)

L= 111.319 * cos (28°)

L= 111.319 * 0.8829 = 98.2835 km (ans)

(c) Earth complete one rotation around its axis in 24 hours, completing 360°. Then for 1° it will take (24/360) hours = 1/15 hours.

At 28° latitude, earth’s speed = 98.2835 /(1/15) = 98.2835*15 = 1474.2525 km

As The ship going in west direction, the earth’s velocity will get added to its own velocity,

For maximum resultant speed, when ship takes 18 sec to pass 50 m distance, then speed = (50*3600)/18 = 10000m = 10 km.

For minimum resultant speed, when ship takes 20 sec to pass 50 m distance, the speed = (50*3600)/20 = 9000 m = 9 km.

Therefore,

Minimum speed of the ship = (1474.2525 – 10) = 1464.2525 km per hour.

Maximum speed of the ship = (1474.2525 -9) = 1465.2525 km per hour. (ANSWER)

(d) In 120 hours, Ship will travel in km shown below

Resultant minimum speed is 9km/hr. So in 120 hours, it will go about (9*120) = 1080 km.

Resultant maximum speed is 10km/hr. So in 120 hours, it will go about (10*120) = 1200 km.

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